I tried a one shot with every check as 2D10 rather than 1D20, as a test run and thought of reporting it here. My players were the usual people I play with as GM or PC and veteran gamer in tabletop RPG and board-game.
As a result the checks throughout the session seemed to be resolved with more ease, but I think it's a matter of how it felt rather than a statistical result. Indeed the players all have computer related job which gave them technical insight on the consequence of switching D20 for 2D10s and with this knowledge they planned their actions with a more reliable average result of the dices, securing less bonus to ensure their success (they can get very creative). Personally I felt not much difference for game balance but it might indeed change how some players tackle challenges on. I didn't fell the need to change the base difficulty (including AC) from "10 + modifiers" to "11 + modifiers".
As a whole I think the change can work, but to preserve the original ambiance of D&D/pathfinder style games it should be better to apply it selectively. My original idea was to grant the 2D10 to beat a check when the PC are "competent" in the thing being checked and get them stuck with 1D20 when they are not.
So now I want to discuss the criterion under which to class the PC as competent or not, let's try to get them all in order:
Skill check: Easy one, they should get the 2D10 for class skill with at least one rank.
Ability check: As it works as a skill check (base ability modifier) with no skill associated they should never get 2D10 on such raw power contest, but a case could be made when a class special abilities gives a bonus to an ability check specifically (I'm thinking about some barbarian archetype which gives bonus to break things with strength check).
Attack check: I'm a bit stuck on this one, to gives the 2D10 with the used weapon's proficiency seems a bit too good as everyone would basically have it, but to restrict it to some criteria like a feats (weapon focus seems a good candidate) seems too stringent (and pointless as everyone would auto-take it). Maybe I will chose to apply the former since combat comes with the territory for adventurers, it makes more sense flavor wise to me.
Maneuver check: Easier as it is specialized enough, 2D10 would comes with a feat. The question is to make it part of the existing feats which levy the penalty for attempting the corresponding maneuver, to make it a custom feat with the former as a prerequisite or maybe part of the "grater [insert maneuver]" feats benefits (a bit too limiting in my opinion as they all have a BAB +6 prerequisite).
Save check: I would simply replace the benefits of the "improved save" line of feats (one re-roll on the corresponding save per day) with the benefit of granting 2D10 on the corresponding save check (powerful but still needs to invest two feats).
That's all I could thought of for now. Please give me your take on this: is it a good idea, is it balanced enough? Did I forgot some checks which needs to be decided upon, does some criterion needs clarification? Any feedback is welcome.