And shouldn't it? Doesn't it even use the third person model?

It uses the third person model. I'm not sure at which point the glow is applied to be missing in this case, and if it where to work, it might just clutter the screen really badly. Will have to check, but might be a case of "it's better turned off" like with the F3+B hitbox in firstperson.

Even if it is, can you make it optional via config?

I mean, Maybe. Why would you want to make it worse tho?

becuase i like realism, but in case it looks bad and other people dont, then it should definitely be toggleable

Just tested it, player renders in the pure team color(white by default), and I think fixing that would require MixinExtras which I won't look into rn due to old mc versions and Forge/NeoForge.