For me, roll&keep is not the most intuitive dice system (dice pools and simple d100 are). It works great in some situations, though.
IMO, the best use for R&K is when a test is affected by two mostly independent traits that are both important for the activity. For example, if characters use robotic bodies that may be easily switched, character's combat skill and body's speed, resistance and weaponry are such traits.
A "classic" approach with the traits added together doesn't work here, as it would make a character with one trait high and the other low as good as one with balanced traits. Using "roll skill, keep stat" gives the desired effect. Also, it emphasizes higher potential of high-stat characters and predictable efficiency of high-skill characters, which is good if one prefers realism.
The analysis above shows that I like to fit mechanics to what it represents. For this reason, I don't find "generic" systems interesting. I use mechanics to empower the style of given game: sometimes tactical combat, sometimes fast martial arts action, sometimes immersion in strange cultures, sometimes mind-shattering horror. If the system does not give me tools for the important part, or forces me to spend time and attention on something that is not my focus - it is not worth using.
In other words: I suggest you forgo the idea of making a generic system. Decide on the style and focus (and maybe setting) of your game, then create a system that fits it.