I think you need to reread the counteracting rules. You NEED to be heightening Dispel Magic to deal with higher level effects, because counteract checks and their degrees of success rely on the relative level of effects, and the counteract level if dispel magic is based on spell level, not caster level.
What you can counteract depends on the check result and the target’s level. If an effect is a spell, its level is the counteract level. Otherwise, halve its level and round up to determine its counteract level. If an effect’s level is unclear and it came from a creature, halve and round up the creature’s level.
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Dispel Magic is used to counteract spells. Counteracting in general requires a check.
Critical Success Counteract the target if its counteract level is no more than 3 levels higher than your effect’s counteract level.
Success Counteract the target if its counteract level is no more than 1 level higher than your effect’s counteract level.
Failure Counteract the target if its counteract level is lower than your effect’s counteract level.
Critical Failure You fail to counteract the target.
So if the level of your Dispel Magic casting is too low, it cannot succeed at counteracting the magical effect, even if the counteract check is successful.
Dispel Magic not only benefits but requires Heightening in order to be useful.
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Step 1. A 5th level wall of fire exists. Its counteract level is 5. Let's say that it was cast by Bob who has DC 27.
Step 2. Alice wants the wall gone. She casts level 4 dispel magic, because she's only level 8. Her counteract level is 4. Her spellcasting modifier is +16.
Step 3. Alice rolls a D20 and something happens. If he rolls an 11, for a total of 27, she meets the DC. With a success, she can counteract an effect one level higher than her level 4 Dispel Magic, like a level 5 wall of fire.
3A. If Alice had cast a level 2 Dispel Magic instead, she would need to critically succeed to counteract an effect 3 levels higher than her level 2 spell, and could never counteract a level 6 or higher spell, regardless of her roll.
3B. If Alice had used the wand of 6th level Dispel Magic that was lying around in the Chamber of Macguffins, she would counteract an effect up to 1 level lower than her 6th level spell (again, like a 5th level wall of fire) even on a failure.
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Sure, I'll give it a shot.
Freddy the Fire Mage cast a Wall of Fire heightened to level 5. Freddy is a level 9 wizard with Intelligence 19 and Expert arcane spellcasting, so his spell DC is 10 + 4 + 4 + 9 = 27.
Clark is a level 7 cleric who wants to dispel that wall. Clark has a Wisdom of 19 and is an Expert at divine spellcasting, so his spell attack has a bonus of 4 + 4 + 7 = 15.
Clark is going to counteract with Dispel Magic so he uses his spell attack bonus to make the check. He is going to counteract a spell so the DC he's rolling against is the spell DC of that spell. So Clark is rolling 1d20+15 against a DC of 27. He needs a 12 to succeed, he fails on a 3-11, critically fails on a 1 or 2, and critically succeeds on a 20.
The results section in the Counteracting rules tells us what happens on each possible result:
Critical Success Counteract the target if its counteract level is no more than 3 levels higher than your effect’s counteract level.
Success Counteract the target if its counteract level is no more than 1 level higher than your effect’s counteract level.
Failure Counteract the target if its counteract level is lower than your effect’s counteract level.
Critical Failure You fail to counteract the target.
So if Clark rolls a 12+, he would get a success, and that would counteract the spell as long as it's no more than 1 level higher than his own Dispel Magic effect. Since in this example we said that the Wall of Fire was heightened to level 5, Clark will remove it when he rolls a 12+.
On a failure, Clark counteracts the target only if the target is 1 level or more lower than his effect. In this case, that's not good enough.
Now suppose that Clark also prepared a not-heightened Dispel Magic, so a level 2 Dispel Magic. If he uses that to try to Counteract the Wall of Fire, then he needs a critical success, because level 2 + 3 from the crit is enough to counteract a level 5. That's much harder!
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But suppose Fred had also cast a Slow spell on Clark's friend Bob. Slow is a level 3 spell. If Clark casts his level 4 Dispel Magic on that Slow spell, and fails the Counteract check, he can "only" counteract effects of a level below his Dispel Magic. But that's still good enough to get rid of the Slow.
So the big idea here is that it's much, much easier to remove low level effects. In fact, it's very reliable that you can remove low level effects. If you're prepared to pay more, by using a high level Dispel Magic, you only fail to counteract a lower level spell on a critical failure.
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Counteracting is a big part of the more advanced strategy for caster characters. It encourages using high level spell slots (because they're harder to counteract) and it encourages high level counteract spells (because they reliably remove low-level stuff).
One interesting phenomenon is that in many encounters where there's some kind of magical hazard, the hazard itself isn't the highest level opponent in the encounter. Like, a level 7 party might run into a fight with a level 8 monster and a hazard with a counteract level of 3. Then if you use your level 4 Dispel Magic, you will almost certainly shut down the hazard, and at a comfortable distance (120 feet). Shutting off what is basically a "lieutenant" level enemy with one spell is actually pretty good work!
A negative consequence however is that bosses with dispel magic will absolutely wreck your buffs. Count on needing extra castings of Fly to get to the flying wizard boss because he can dispel a couple. However, that does keep him busy and if your caster is trading actions turn for turn with the boss, that might give the rest of the party an action advantage.
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The key part of the rules is the 'success chart' at the end of the entry: Source
Core Rulebook pg. 458 2.0
When attempting a counteract check, add the relevant skill modifier or other appropriate modifier to your check against the target’s DC. If you’re counteracting an affliction, the DC is in the affliction’s stat block. If it’s a spell, use the caster’s DC. The GM can also calculate a DC based on the target effect’s level. For spells, the counteract check modifier is your spellcasting ability modifier plus your spellcasting proficiency bonus, plus any bonuses and penalties that specifically apply to counteract checks. What you can counteract depends on the check result and the target’s level. If an effect is a spell, its level is the counteract level. Otherwise, halve its level and round up to determine its counteract level. If an effect’s level is unclear and it came from a creature, halve and round up the creature’s level.
Critical Success Counteract the target if its counteract level is no more than 3 levels higher than your effect’s counteract level.
Success Counteract the target if its counteract level is no more than 1 level higher than your effect’s counteract level.
Failure Counteract the target if its counteract level is lower than your effect’s counteract level.
Critical Failure You fail to counteract the target.A 2nd level Dispel Magic:
- Can NEVER dispel a 6th level or higher spell
- Can ONLY dispel a 4th or 5th level spell if you get a Critical Success on your Counteract check
- Can dispel a 2nd or 3rd level spell if you get a Success (or better) on your Counteract check.
- Can dispel a 1st level spell if you get a Failure (or better) on your Counteract check.
- If you get a Critical Failure on your Counteract check, you don't dispel anything.
Looking at the actual Dispel Magic text, i can see where your confusion is probably coming from: The use of the phrase 'If you succeed against a spell effect...' is more than a little awkward, but I believe it is trying to say 'if your counteract check scores a high enough result to counter the spell or effect...'
As a side note: if you're using a virtual tabletop to play (like Roll20 or Foundry), I would recommend treating dispel magic as an attack spell that does no damage, and also add the counteract results table in its description. That way, the VTT app will automatically roll your counteract check, and you can quickly figure out what level of effect you can dispel.
The same goes for other spells that can counteract effects, like remove fear, remove paralysis, neutralize poison and quench.