Just a few comments....
in no particular order....
1) It may well be that the intention of the skill categories was to remove the need for most stat-based rolls when RM2 was revised into RMSS. The category skills do tend to aid in that respect.
2) Not all of the categories are well suited to this idea, and some categories don't even have bonuses.
3) I can easily see some stat-based rolls that might require 2 or more stats based on its complexity or details (i.e. such as trying to throw another party member high enough for him to grab a window sill -- that would be strength and agility (just as with thrown weapons), but there is no real skill that applies to the thrower).
4) The whole reason for having stat-based rolls is to allow for the players to be able to roll
something when a situation comes up for which there is no specific skill (or where an existing skill cannot be adapted/co-opted for use).
5) Using skill categories in place of stat based rolls is nothing more than replacing one roll with another, but the replacement has the benefit of the character's being able to improve through the purchase of skill ranks, so it allows for more experienced characters to be better than lower level character at the same sort of rolls.
6) The problem with using skill categories is that, IIRC, they only get a single stat, not 3x the stat), so this means that they will start off being much weaker than a regular stat-based roll. So, you end up with a different problem than the one you are wanting to solve, but it also
7) Approximately the same thing could be done by giving the characters a +1 to stat rolls for each level that they have, and another +1 per level if the stat is one of their prime stats for their profession.