I think that’s only partially true as the emitter is not an infinitely small point source. So you’d have to make that center diffuser a LOT larger than you think you do.

There are hybrid reflectors - reflectors that have a TIR either molded into, or suspended in the center of, or integral with, the reflector. A textured or patterned reflector can help a little too, and many of these hybrid reflectors have a patterned surface.