I'm 100% a fan of Tilly & Mary Wiseman, in either universe.
Those who can't see the point of Tilly, beyond comic relief, are sadly blind themselves. Elaboration to follow.
First, Tilly serves to humanize the whole crew, and Burnham in particular. She wisely gets Burnham to talk with her (you must have a lot of other friends) & is the first to accept her, despite Tilly being a social outcast too and wanting to fit in. She breaks the rules to help Burnham with the Tardigrade & at other times. She starts Burnham & Ash down their road. She is the social/human conscience of the show like McCoy was on TOS, Tripp on Enterprise, etc.
Tilly also serves the everyman/young person role. Like Checkov/Wesley/Jake-Nog/Kim on previous Trek shows.
Furthermore, she does this better than those previous roles by not only being funnier, but also because she looks like a normal person. Unusual in Trek for a female character (both Uhura's, Troi, Tasha, Dax, Kira, Kes, Seven, T'Pal) who is dressed like a regular crew member (DIS is the first Trek not to dress up at least 1 female lead differently). It enhances her everyone persona.
Lastly, I am pretty suspicious of those who don't seem to get any of this & instead bash her appearance and/or make statements that are factually incorrect (no cadets on ships: Nog, Enterprise in Generations, DS9 episodes, etc).
Look, it is fine to disagree on a character. I seek not to chill discussion. But Tilly's character does have a purpose beyond comic relief & sunshine (Phlox was the ENT optimist) & we have had cadets before. Those are facts.