It would take extra electronics, specifically an RF transmitter in the TV and receiver in the remote. The receiver in the remote would draw the batteries down faster, and the whole system would mean the set has to pass extra approvals.

I think some system like this would be good. Once in utter frustration, I made a six-foot-umbilical out of packing tape to fasten the remote to the corner of the couch. The remote could only move a smaller amount, but I could always find it.

It wouldn't have to be RF, though RF would work better than some others.

The two systems could communicate with IR blinks or ultrasonic sound. The IR would be a problem when the remote is under the couch cushions or in the next room. I know ultrasonic is limited, too.

But even it it needed to meet Part 15 for RF, it still might be worth it.

Been done on cordless phones. Shouldn't be too much of a hassle to maybe add a tiny speaker and figure out some way to miniaturize and lower the power draw on the receiver.