Specifically, one who rolls to hit with Dex (as fists are finesse), not caring about Str damage that much, while only taking "passive" class feats and no stances which modify AC, that is.
I just want to know if a Str 14 -> 20 & Dex 18 -> 22 stat spread is not awfully crippled compared to the contrary...
Yes, it's viable, and some of the Stances give the best finesse weapon options available. You'd also have an excellent AC even w/o an AC bonus from Stance. Not sure how "passive" you mean w/ your feats, but while damage would be mundane, Stunning Fist could lay on one of the best debuffs in the game for no extra actions if that qualifies.
You should still bump Str up to 18 eventually as you've noted, and perhaps find sources for more damage, like Sneak Attack via Rogue MCD. In some ways you'd be like a ranged attacker: able to attack most anybody, but for less damage while also able to stay away from threats. You don't have to though since you'd have the defense/hit points to tank better than anybody except a Champion/shield Fighter (who pay for it in other ways). Monks are very difficult to hinder from getting in their Flurry.
I'm actually a bit surprised at the question, since many suggested builds prioritize Dex, being as that's such an immense boost to defense. Putting Str secondary does hinder Athletics, a luxury Monk's can indulge in since it's easier for them to have a free hand. But if primarily Striking, that's not a big loss, and Assurance would work fine for tripping oafish enemies.
I just want to know if a Str 14 -> 20 & Dex 18 -> 22 stat spread is not awfully crippled compared to the contrary...
When you said ignore strength I thought you were gonna be at 10 or domething. This is just investing in strength, spreads like these are much better than the reverse for monks due to their unarmored defense.
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I ran a dex monk from 1 to 11th. I picked up Tiger Style and didn't have many problems in combat aside from the usual PF2e difficulty (and a lucky GM that sometimes made my slightly higher AC meaningless).
The thing is, as long as you're not trying to fail with your Monk character, you'll end up with a good build. Which is what PF2e is all about.
So at 20th level, a tiger style dex monk (for example) will be rolling 4d8+1d6+1d6+1d6+8+StrMod with the variable being between -1 to +5, so your strength doesn't really matter for this (it will matter if you want to use athletics though).
At 1st level this character rolls 1d8+StrMod, with the variable ranging from -1 to +3. So your strength mod does matter.
At some point between 1 and 20 the switch will flip and you won't really care about your strength anymore, but at low levels you might feel it. You are better off at 10 strength than a swashbuckler initially, since you get d8 finesse attacks and they don't.
You are better off at 10 strength than a swashbuckler initially, since you get d8 finesse attacks and they don't.
A swashbuckler can start with a d8 finesse attack: Elven Weapon Familiarity or Unconventional Weaponry for a Elven Curve Blade does the trick.
Aldori sword too, plus it's 1 handed.
Normally when people ask the question, they're asking if they can completely ignore strength, and you are not.
Starting at 14 strength is going to reduce you damage by an amount which will be noticed at low levels, but as you get to higher levels the damage dice you will have will have a much bigger range on how much damage you could deal and eclipse the impact of strength. I don't know exactly where this happens, but by the time you're rolling 4 damage dice (and not just weapon damage dice but elemental damage from runes) you're probably not going to care about your damage from strength too much.
So yes, this is definitely viable and shouldn't be a big point of worry.
You will have better defense in exchange for slightly lower damage. It will be enough to carry you to higher levels though.
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Early on, the monk's 'armor' proficiency gives them a +2 bonus over most melee classes. This amounts to having leather armor and then going with a dex build, only you don't deal with a max dex. So with 18 starting dex, you are doing better than anyone with a breastplate.
By the time you hit the dex cap, a dex monk's AC is some of the best in the game and only falls behind champions, really.
Strength is nice, but it isn't everything. With 14 or 16 str early on, you don't really see much benefit with taking it further. Most of your damage comes from magic items giving you more damage dice.
If you feel there are problems with your damage, there are much better options than strength- or even more monk feats. Flurry of blows gives you great action economy for your attacks, so you could easily slot in things like a bard dedication to snag inspire courage. That would give much more direct boosts which also benefits the party.