Yeah, the really low DCs get a bit off, partly because the variance is reduced, but also because 2d10 is not quite centered properly. I could definitely see adding 1 to all DCs 10 and under. If you do that, DCs that RAW you'd need a natural 5 to meet give you an 90% success chance with 2d10 (assuming you now need a 6), instead of 80% with 1d20. On the flip side, DCs that require a natural 17 have a 20% success chance with 1d20, and a 10% success chance with 2d10. So what were the outer 40% of outcomes are moved out to the outer 20%, making the modifier mean more by virtue of really good or bad luck both being less common, without actually changing it.
Consider 4 characters at level 5: A is an average Joe, with a +1 mod and no proficiency in a skill. B is skilled, with either a +1 mod and proficiency or a +4 mod and no proficiency. C is a specialist, with either a +1 mod and expertise or a +4 mod and proficiency. D is a master, with a +4 mod and expertise.
At level 5, with a 2d10 system and a DC 15 check (so, somewhat difficult but not crazy), A has 28% chance of success, B has a 55% chance, C has a 79% chance, and D has a 94% chance. Essentially for this fairly difficult but not crazy task (at the difficulty where you'd expect a non-proficient character to be challenged and proficiency to be a significant boost), proficiency is worth nearly twice as much as it is RAW. Meanwhile, expertise not in your ability score wheelhouse isn't adding quite as much as proficiency at this difficulty level, but it's close -- whereas expertise in a skill that uses your main stat yields diminishing returns, and is worth only about half as much as proficiency was. So this looks about like @
dnd4vr wants: proficiency is rewarded, but being "overqualified" is not worth as much more as being qualified in the first place.
But take these same characters with a DC 20 check, and the picture is different: Now A has almost no chance of success (3%), B has a 15% chance, C has a 36% chance, and D has a 64% chance. So now just plain proficiency helps a bit, but it doesn't really cut it: you either need proficiency and a good ability mod or an average ability mod and expertise to have a reasonable chance, and if you're a master, it's still a challenge (you still fail more than one time in three) but you've got a good shot.
This all looks right to me: something that is very difficult is very difficult even for proficient characters, still fairly difficult for specialists, and semi-reliable success is only attained by those who invest both in the ability and in expertise.