Thanks for your addition, Skyscraper. When I re-read my post I realized I was kind of vague and you filled in the details of how the mechanic works, which my post was sadly lacking.
The only question that came up in my short gaming experience, is when to do an ability check (1d20) where the 1d10 vs 1d20 question doesn't come up; and when to have a skill roll where the 1d10 vs 1d20 question comes up. For example, if the fighter wishes to sprint to the other side of a clearing, do you do a STR check (1d20 + STR) or an untrained skill roll (1d10 + STR)? Likewise, if he wants to break a locked door down?
I like to think that specific trumps general. If a person has a specific sprinting ability that would become the default, but without such we would default to a STR check. In other words, abilities gained through background profession can actually be useful if the situation merits.
In general I don't do much with skills and typically default to stat checks. One thing I tinkered with was the notion that a player could pick 3 advantages or things he does well and it would be a lot like having 3 skills per character. They could pick anything from a 3E rules set or whatever, but then I would allow them to have a bonus to their roll if those skills were useful in the adventure. One warning, however, is to be sure that players can't pick combat bonuses or other abilites which might prove to be too advantageous. (We all know that players are clever, however, and sometimes they out-think how they can use a skill which seems pretty tame at first. Darned clever players!