It makes you realise just how well designed the default outfit is, it fits the world perfectly. It’s different yet natural and clearly signifies that you are playing an AC game while still not being a rip off of any others AC outfit. The same can be said about Ezio’s outfit, it just fit Italy. So when you bring an out specifically designed to fit AC Brotherhood, a game set in Rome, it is naturally going to look out of place because it is.
This then extends into their personalities. Ezio was a rich man with rich friends and his outfit reflected that. It was fashionable and made him look important. Bayeks our fit was made of random clothes to fit his lost personality, both in terms of him not having a home and his mental state.
Tl;dr: Ubisoft are experts on outfit design.