I think that systems like these tend to be problematic. The first problem that can occur is over-specialization. For example, while a character in Front Mission can go into battle equiped with a missile launcher, a melee weapon, and a machine gun, it is very, very hard to be good at all three. In this case, the biggest problem is that the weapon skills that boost these weapons build up in a linear fashion. For example, a typical pilot specializing in guns on my team right now has 8000 experience points in his Short range combat skill, and is thus about rank 80 in the skill. My only character who has split his focus on all three main combat skills only is at rank 40 in the Short range skill, and only around rank 20 in the other two. Even my character who specializes mostly in Short but sometimes uses Long range missiles has his skill ranks at 59 and 27 respectively.
And the effects of these skill ranks add up. For example, one of my Long range experts, with a skill rank of 80 or so, can destroy an enemy mech's arm by hitting with just one of a volley of three missiles. My main character, who has a skill rank of about 20 with Long range missiles, has to hit with all three missiles in the salvo to destroy the same part. Because the progression is linear, a character who splits his attention between two skills will only be half as good at either one compared to a specialist. And in the long run, the net effect of this difference will continue to add up to be bigger and bigger. So, this system forces extreme specialization, at the risk of gimping your character is you do not.
The risk of a character being gimped is the biggest flaw in a system where statistics build up through use. In a traditional leveling system, it is easy for the game designer to predict what the stats for a given character will be at a given level. Thus, the designers creating the monsters for a given dungeon or battle can figure out what stats to give the monsters, using the expected level of the player's characters. However, in a system where stats level up based on use, it is much harder to predict what the characters' stats will be. Thus, the balance of the game can be seriously thrown out of whack.
Another problem can occur when character's stats level up based on parameters the player does not have direct control over. For example, one of the four stats in Front Mission is Evade, which only goes up when the player defends against enemy attacks. However, there is no effective means of controlling who the enemies attack, so how fast this skill builds up is completely up to chance. This is an even bigger problem in the much older Final Fantasy 2, where characters only gain more hit points and defensive stats by being dropped to less than half health in a battle. As a result, the only way to have high enough stats to beat the game involves having your own party members beat on each other. Thus, getting good stats requires a lot of needless work.
In order to limit these problems, it is necessary to step away from a pure "stats build up as you use them" approach. All of a character's necessary stats should be able to grow to some degree, regardless of whether they are used or not. For example, a character who only uses offensive skills should still build up defensive stats, even if they do not build up as much as offensive stats. Furthermore, tweaking the system so that a character who uses multiple kinds of ability can stay within 70-80% effectiveness compared to a specialist will prevent characters from becoming gimped by early mistakes.