OK, this is a joke but it does point out the important stuff.
We all know the contact points and there locations are important. Some say all-important. But .. without a suitable frame, keeping that BB, seat and cockpit in their proper locations in space s very difficult! You could make a stand for the BB and put the seat and handlebars on tables, but that's all going to h*** when you try to get on the seat!
Beyond that, the frame on a trainer matters very little. Correct dropout spacing for the rear wheel. A WB cage might be nice. Now there is that important few inches of matter between the ears. A better frame might make a difference there and that could influence the electrical signals from brain to leg muscles and hence the quality of the workout.