The controller is responsible for their airspace and they need to be able to accommodate everyone whenever possible.
The reason for denying any aircraft is very situational, it may be difficult to tell why you are denied, so to say you were denied because you are a certain aircraft type is jumping to a conclusion. If you get a “no light aircraft” command sent your way, well then sure. That’s where the education comes in, you have to ask the controller to find out why they sent you a specific instruction. You can on the forum, here is our directory.
It must be specifically reserved for airports that do not accept light aircraft IRL (e.g. EGLL, OMDB, VHHH etc), as 4.2.1 says in the ATC Manual.
My most memorable moments controlling has been fitting in slower performance aircraft in busy airspaces.
We service the pilots they don’t provide a service to us. You just got to work with what you have and fit them in, it’s part of the fun.
References: 7.1.6 of the ATC Manual