True. Certainly, learning and application of gained knowledge is the only way it could work at all.
[Warning: 
]However, I'd argue that there's often much less overlap in gaming then there are in physical pursuits. For example, consider two fairly disparate martial arts: jujitsu and muay thai. Would training muay thai make you better at jujitsu? Not at all in technique, but your endurance, hand-eye coordination, and strength would all most likely increase, thus improving your jujitsu.
Even here, however, there is less overlap that first seen. First, the important part of jujitsu is not strength but technique, which is completely ignored by trying the other art. In addition, some techniques learned in muay thai may actually hinder you in jujitsu, as you will have to rebuild your muscle memory.
These technical aspects I see as being most akin to the games we play. When two games share a common ground you could certainly gain skill by practicing both instead of one - take Pathfinder and 3.5 for example. The two systems are similar enough that if you spent time optimizing one it's pretty clear you'd have a good sense of what the other offers as well. I see that as akin to your judo/aikido example - the similarity in techniques gives you a greater benefit.
On the other hand, even in similar 'fields' you can often have very little overlap. Sure, I learned a lot in that aikido class - but my time would have much been better spent practicing judo for the same amount of effort. Perhaps if you've completely exhausted your knowledge and creativity with regard to a specific subject (which is quite unlikely to happen), then time spent on a different system could benefit you - but it might not. It related heavily to your own creative process and how best you can come up with ideas - which might be best spending gaining experience in the very system you feel you've exhausted.
I think a somewhat clear measure of what a good player is is also important. On what basis do you say 'you would be a better player if...' without being able to, at least in a general sense', quantify what a 'better player' is? Optimization is subjective in almost every case, because games are subject to the whims of the players. You have subjective limits set on you in every scenario, whether that be social rules or simply the limits of the game system itself.
I guess a reasonable definition would be - 'A good optimizer is a player who, given a system and a set of guidelines on building a character, is able to build an effective character within that system that follows the given guidelines as closely as possible.' I don't think this is something that is necessarily improved by learning other systems, though it can sometimes be.
