So, my main considerations for a skill system are:
1) Space spanning - Does everything that a character would try to do have an obvious choice of a skill that would cover it? This is pretty obvious. Players should be able to tell from the skill list what sort of things they'll be called on to do, and whatever the players attempt should have some sort of skill that covers it.
2) Discrete - Does each skill represent a truly separate area of skill? Skills should not overlap, nor should a skill be built around something that can also be covered by a combination of other skills such that a person who has all the skills we would expect going into doing X find themselves unable to do X because it has its own skill. For example, if 'Knowledge of the Law' is a skill and 'Bargaining' is a skill and 'Oration' are skills, then Lawyering probably shouldn't be a skill. Lawyering should probably in such a situation be a 'Feat' or 'Trait', ei "Gain a bonus to skill use when you use them in in a professional legal situation." and not a replacement for the discrete skills themselves.
3) Independent - This is like discrete but is the additional test that advancing each skill is not connected to another one so that it makes sense that you could advance one without advancing any of the rest. For example, I very much dislike it when a system has a completely separate skill for using clubs, hammers, and maces as weapons. It doesn't feel to me sensible that I could get very good at using a baseball bat as weapon in combat, and advancing that skill would not make me more comfortable with a mace than a person who had never held a swung bludgeoning weapon of any sort.
There are a ton of ways you could cut apart the skill space into discrete and independent pieces, and there are skills that may or may not be relevant to every setting, but every skill system should be trying to obey those three things. Notably GURPS doesn't obey the above considerations and it results in a system that is highly arbitrary and almost unusable because it has to kludge together so many solutions to the problems involved.
As a practical matter, the number of skills in a skill system that obeys the above constraints tends to be neither small nor large. If it's too small then either skills aren't space spanning, or the skills are so abstract that they aren't discrete. If it's too large, then the skills tend to be neither discrete nor independent.
Where I tend to cut the talent space up is when you can raise the objection that you can imagine a person who is good at X but terrible at Y, then this tends to imply they are separate skills.
Note that the additional complexity of having a skill system isn't required. You can just get by with abilities and traits. However, if don't have a skill system then your ability system has to meet the three requirements above.