Gadolhadorah
Chazal bring it in the third perek of Bava Basra.
While that isnt the exact case here. Chazaka does have broad implications in halacha in particular regarding mitzvos like servign as chazan or Baal tokeah. Daveinig in shul is a mitzva too, and the concept of Chazaka, without question exists.
Of course a Shul can make their own policy.
“especially after a certain point in the davening whether it be baruch she’amar, nishmas or borchu..”
I prefaced my first comment as not referring to late comers.
I agree it is wrong for late comers to ask people to move, though even thenIfthey ask nicely AND ( cant stress this enough!) provides a seat I think it could be justified but not as easily as the guy who comes on time.