I assume that Bats has studied all known fighting styles and only mastered like 3 or 4. I mean, if he's fighting a dude that knows Chilean toe fighting, he'd recognize it. Know what it is just by seeing a guy use it, but is Batman a master of Chilean toe fighting? Of course not.
Well, the problem with that is that even it is unnecessary. While the different fighting styles of the world are, obviously, different from one another, it's not to such an enormous extent that not having tudied, say, Tae Kwon Do will put a Kung Fu master at a disadvantage if they fight a Tae Kwon Do master. Blocking a strike is blocking a strike, regardless of the style, so it's not like you need to know Tae Kwon Do blocks to block Tae Kwon Do strikes. The primary difference between different styles if how much they emphasize different kinds of strikes and different kinds of movements. Tae Kwon Do, if we are to use it as an example again, puts an enormous emphasis on kicking.
In which case you might say that it would be useful to stufy every technique known to man so you might have an idea of how one fights fairly early on in a fight, but even that isn't as useful as it sounds, because even in a specific style there will be variations based on the body type, level of experience, and general physical limitations of the fighter. For example, I study Kenpo Karate, which generally puts an emphasis on critical knee strikes and kicks to sensative areas and using momentum and inertia in your favor. I'm very tall and fairly strong, and not exceptionally graceful, and so I tend to favor grappling and using my size and weight to my advantage. Other, smaller and lighter practitioners, prefer flurrying kicks and attempting to tire out their opponent by remaining elusive. Even within the same system there are a wide range of styles based on the individual.
And as for knowing a multitude of styles for your own benefit, the fact is ultimately it is very redundant. There comes a point where kicking someone is just kicking someone, regardless of the manner you go about it. And because different techniques favor different phsyical strengths and limitations, Batman, or any fighter who studies multiple styles, will end up favoring the moves of one, maybe two styles, over all the others because they are the ones that fit their body type and physical limitations.
Now, it is true that studying multiple styles can give someone a broader idea of what they are capable of in combat, I know that even in my Kenpo Karate school we have looked at techniques from boxing, Tae Kwon Do, and Krav Maga, but it ultimately would not be especially useful to master one style, and then master another, and then master another. Instead, it would be better to find one style that fits your body to work from as your core style, and then study other styles to borrow techniques that can be seamlessly woven into your personal style so that you may refine your technique.
So in that sense, yes, someone like Batman probably would study many, if not most, common hand to hand combat styles. But the way most comics portray it, with him having mastered every form of hand to hand combat known to man, it;s just an ill informed attempt to make him sound badass that sounds absolutely ridiculous to someone who knows anything about fighting, even someone like myself, a total novice.
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