As far as i know there is no canon reason why most races, not just starfleet, didn't use carriers.

But out of universe - The reason why carriers were never seen was primarily a budgetary issue: filming and animating multiple fighters is expensive. So having single ships was easier to work with. Thus Star trek shows never really did carriers.

DS9 got better with fleets, but each ship tended to move in the same direction and so with CGI it was easier to do. The expensive scenes were where you have multiple ships moving independently and doing their own thing. Someone has to go in an animate each one.

Babylon 5 also had larger fleet battles with multiple independent ships. But being entirely CGI based they weren't as restricted as the model-based star trek shows of the time so Babylon 5 could do more.

Today, you may yet get your wish. CGI has become much cheaper and and computer gaming AI can be substituted to create believable battles without needed too much animator time and cost.

Maybe now it will be an option.