Flexibility.

It is not required, I don't think it is ever required in any martial art (except maybe ones that actually involve it, like say capoeira and some kicking based martial arts)

It is just good for you, without flexibility you end up having lots of vulnerabilities other martial artists may not have (for example you are more vulnerable to choking and joint locks, and you will find it harder to break free of these kinds of attacks than otherwise if you were flexible) and you will end up in situations where you cannot execute certain moves very well (or at all) because your legs don't bend enough.

I'm sure the focus on full split is probably because for most people, their legs tend to be far more stiff than anything in their upper body, and even with a stiff upper body, you can usually get by pretty well (but you won't be any Floyd Mayweather, do you think he could dodge like that if he wasn't super flexible in both his upper and lower body? He's a boxer, but I bet he can still do the full split even if he doesn't really have to to be able to box well, his style requires it)

Being flexible increases your range of motion, and the efficiency and speeds at which you can move within said range. For example, you may find the range of your punches and kicks significantly increasing thanks to your flexibility (especially the kicks, the punches might improve, but this will be much harder to notice).

And in any fight (inside or outside a ring) being flexible simply increases the range of options you have for every situation, while reducing how predictable you can be to your opponents whoever they may be (especially if you're not in a ring, against an opponent that hasn't studied you, they'll be pretty surprised if they see something like an axe kick, and that may intimidate or confuse them putting odds in your favor)

In the end, let's just look at the basics of a flexible vs stiff body.

When you're stiff, it can be a bit of a struggle to bend at your hips or your knees (so reaching for something on the floor, or tying your shoelaces, it becomes a bit harder to breathe and thus a bit harder to move in any sort of way until you are upright again). When you're flexible all of that goes away, you can easily bend over without struggling, straining yourself or noticable breathing difficulties, and the more flexible you are, the more you can bend without these breathing difficulties which gives you a greater range of freedom for what kind of awkward positions you may need to fight from (I mean come on, the shapes you get bent in when fighting on the floor can get pretty intense, and if you're not flexible, that may just be the end for you).

Your flexibility in your upper and lower body matters, that's why you want to be able to do a full split, but you don't really have to be able to do it when you start, only when you're reaching the higher levels of mastery where new moves are getting more and more complex and harder to execute.

So in short, flexibility as you could guess increases your versatility, and this is crucial to any martial artist, being able to fight in unexpected ways that most normal people probably couldn't do to begin with.

My advice to you if you're a beginner is to work like hell to attain that flexibility, but do it while you're training in your martial arts of choice, don't put martial arts on hold because you can't do this yet. Start doing it with the intention of being able to do it later, and don't just work towards splits, work towards flexibility in all areas of your body (hips and waist are just as important as your legs), perhaps above and beyond whatever you get in actual martial arts classes or in your regular training sessions, and for your own safety, remember to try to keep your flexibility balanced (very few things will be more annoying than being noticably more flexible in one leg than the other, or on one side of your hip than the other, the same applies of course to strength, you don't want to have a stronger right leg than a left leg, or right arm than a left arm, balance is important, and if you ignore that you will pay for it later on, unless you were never really serious about martial arts or just keeping your body in a good shape to begin with)