The only problem I've encountered with that approach is when players don't pick a representative skill to stand in for a particular attribute. For example, if you don't have a skill involving strength or some aspect of physical prowess then you need to decide how to deal with a situation where raw strength is needed.

I've used "phantom" attributes to cover this: the players need at least one skill relating to each of Physical, Mental and Spiritual, for instance; other than that they take whatever skills they wish. It avoids having a fundamental gap at the heart of the character.

OVA:The Anime Role-Playing Game is a rules light rpg without attributes. The way they did it was to just assume you're average unless you take skills/gifts/faults/whathaveyou that modify it. So, if you're playing as a 17-year old high school student, the base assumption is that you're middle of the road (C grades, not athletic but not unathletic, etc). If you want them to be strong, add that. If you want them clutzy, add that. Basically, you don't have to cover the mundane, middle-of-the-road stuff, just the things that make the character different.

I've run Fudge in both forms before, and will probably continue to use both. That said, I have found three major uses for attributes.

1) The default at Fair instead of Poor makes them useful for nonspecialized traits, as opposed to specialized professional skills and the like.

2) Them being more expensive to advance than skills makes them useful for anything that would be disproportionately useful as a skill.

3) They're a short list, which can make them really useful at briefly mechanically communicating setting or theme for a particular game.

Fate uses a short list of skills and bakes the attributes into skills (https://fate-srd.com/fate-core/default-skill-list). It works fine. If someone doesn't have an aporopriate skill you default.  If it becomes an issue you could look at the defaulting skill web from Shadowrun (1st and 2nd edition).

In my Fudge/Fate hybrid, I use the D&D attributes.  Yep, the familiar six.  Then PC's have five "aspects" like in Fate or the roles in EZFudge.  The aspects define how they use the 6 attributes.

Also, if they want to use an attribute in a way that is close somewhat related to an aspect, they roll at one level lower.  So an engineer knows some science, but not as much as a scientist (and vice-versa) so they roll on INTELLIGENCE but one rung lower on the ladder.  If it is a real stretch, they roll two rungs lower.

Don't know if this helps, but it's what I do.