Will my 28" suitcase require a bigger taxi in Roma?
Possibly
Not all cabs are same size
Why such a huge suitcase?
You’ll have trouble on trains too if you intend to take train anywhere
https://www.ricksteves.com/travel-tips/packing-light/packing-smart
The majority of taxicabs in Italy are minivans or large size station wagons, so your huge suitcase can be easily accommodated in the cargo area. That doesn't mean you should pack such a large piece of luggage. I strongly recommend you limit your luggage to a 24'' suitcase. Actually if you travel also by train you should not go above a 20'' suitcase. 28'' is way too cumbersome.
Come on guys; cut the OP some slack. For all we know she is moving for work or a year of university and not just for vacation. OP, you shouldn't have a problem fitting just you and your suitcase into a taxi.
I took a 28” Antler suitcase and a backpack to Italy for 4 weeks. No issues in taxis. Very easy. No issue on trains. Just be ready to board and depart.
I had a family of 4 for 4 weeks. I didn’t stress about the luggage once.
Also keep in mind, I watch a lot of train videos and not every train car can handle large suitcases either in the vestibules, the overheads or between the seats. Especially when things are busy.