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So for skills especially, proficiency doesn't have as much impact as it should. A characters level in investment should be more than just +1. With +10 being a crit success/failure +2 seems appropriate, difference in level of proficiency has a 20% chance of making a difference on each roll. Adding a new rank in proficiency, Mythic, and you get a +8 difference between Trained and Mythic. This equals the current difference of trained and no item vs legendary with a +5 item = +8. This allows item bonuses to be removed from skills, making the differences between characters more about what they're invested in.
This requires separating skills for things like attack bonus and saves. I feel like that's a good thing, they should work differently and allow more differentiation. A large gap in a skill is okay if every character has a similar amount of skills they're good in, and skills have similar amounts of narrative power. A large gap in combat stats is less nice.
If keeping skills and combat stats using the same system, have each rank in proficiency give a +1 bonus and a +1 circumstance bonus, for a total of +2.
Untrained: -2 or -4
Trained: 0
Expert: +2
Master: +4
Legendary: +6
Mythic: +8
At each odd level starting from level 1 you can increase one skill to Expert. Starting from level 7 you can increase a skill to Master. Starting from level 13 you can increase a skill to Legendary. Starting from level 19 you can increase a skill to Mythic.
Expert at level 1 lets a character focus on something from level 1 and Mythic at level 19 lines up with 10th level spells. Increases in possible rank come every 6 levels, for a smooth increase.
Also:
Using these proficiency ranks would also allow more differentiation between weapon users and spell casters. Currently spell casters can't start with an 18 strength or dexterity so as to not outshine weapon users. This change in proficiency would allow a change in the ability score system to let all characters start with their highest score in whatever they like, while keeping weapon users +1 to hit better than spell casters.
Alternatively, each rank of proficiency could grant a +1 bonus and a +1 item bonus.
This would allow magic items to improve skills without being necessary. If you have a high enough proficiency the items won't improve your bonus, but if you don't have a high enough proficiency, or want the maximum possible bonus, you need magic items.
With this change and these ability score changes the maximum spread between characters would be:
Minimum: -1 from ability score with racial flaw, -2 or -4 from Untrained = -3
Maximum: +5 from ability score using all free boosts, +8 from Mythic = + 13
For a total difference of 16. That becomes 17 if there are +5 items, 18 if untrained is -4, or 19 if there are +5 items and untrained is -4. I believe that is the design goal for maximum possible difference between equal level characters.
A normal spread between minimally and maximally invested characters would be:
Minimum: 0 from ability score, 0 from Trained = 0
Maximum: 4 from ability scores, 8 from Mythic = 12
Magic items could also allow you to count as a certain proficiency: "The Greater Skeleton Key allows you to attempt Master Thievery checks with a proficiency bonus of +X or your own, whichever is higher." That would be another way to make magic items give a numerical bonus, without overwhelming the impact of proficiency.