Does the mouthpiece rim inner-diameter really matter?

Yes, in addition to other factors. 

The mouthpiece rim is often referred to with these three measurements:

• the OD (outer-diameter)

• the high point

• the ID (inner-diameter). 

The alteration of any of these three points will dramatically change how the rim feels and functions. Most brass mouthpiece manufacturing companies provide the ID specification as that is somewhat of an industry standard for rim measurement. 

But what about the other two contact points? Very rarely is the OD, and high point discussed. By moving the high point towards the inner or outer edge you can create the feel of a larger or smaller mouthpiece without altering the inner-diameter. By moving the outer edge inward or outward you dramatically change the surface contact area for your lips.

Lastly, the profile or shape of the rim also affects how the mouthpiece feels.