My party is a fan of dice throwing. A lot. And although they are not analysing things, they prefer visible improvements, like in numbers: proficiency bonus, ability scores, skill scores, etc.
Because of this, I'm considering of removing the 20 cap on ability scores, so they can get over 20 with ASI (exclusively), but usual means of bypassing the cap is also possible.
I'm aware of "bounded accuracy", but I don't see immediate danger of allowing this.
What will happen if I remove the cap? Will the game be broken?
Casters become much stronger
The largest problem I foresee is Save DC.
By RAW, Save DC is soft-capped at 19. 8 + Proficiency + Ability. Without the 20 cap, that goes to 24 or more, raising the save DC to 21, plus bonuses from magic items, specialized builds, etc.
This is a problem because Save DC is tied to a single ability score but can force saving throws for every ability score. Offenses will go up much faster than defenses, making everything bloodier.
Dexterity builds become much stronger
The other major issue I foresee is that this makes Dex builds the best melee builds. AC and Damage and Attack all from increasing Dex, with AC soft-capping around 22 for +3 Leather and a 24 Dexterity; compare that to the Strength build's AC 21 for +3 plate.
There are other issues, but those two are the ones that trouble me most.