It may seem like a dumb question but here goes. If I can program 2-3 models with a transmitter, and use different receivers, when I select a different model, do I still have to re-link the receiver?

I am not sure if this would be correct with your set-up. I have a Flysky 2.4GHZ with 2 different receivers. When i bind to the reciever for each model i am done,just select which plane you want to fly. Just make sure you save the setting for each plane if the servos are setup different under the model name. 

I wont speak for other brands, but you don't have to re bind Futaba radios when you change models. Good Luck, Dave

Nor HiTec.

I'm not sure there is any Transmitter that has multiple memory that needs rebinding.

Think about the RX that you just bound. Does it have any way to know if the TX is used for other things when it's not in use? And the TX memory is there to have the right settings for each plane. So if the TX is set for the right model, the TX-RX pair should work right no matter what the TX has been doing since they were bound.

You bind the RX to the TX after all.

Agreed, all binding does it teach the Rx to only take commands from your Tx. It doesn't do anything to the transmitter.

You'd think, but thats not always the case.