Hi Ed,
I suppose in theory a properly aligned TRF would perform as well as a superheterdyne. That isn't the way it works in real life, though.
In a TRF radio the user tunes every amplifier stage. Since they are tunable they can go out of tune more easily and as such get out of tune with each other.
Also in a TRF set you can have a problem with the different amplifier stages being in tune on some parts of the band and out of tune on other. Sensitivity will vary depending on where you are on the band.
Superheterodyne receivers have their IFs which are tuned at the factory and tend to stay in tune as long as no one fiddles with them. Only two circuits have user tuned capacitors, the front end input and the local oscillator. They need to be consistant with the IF of course, but there are only two instead of the three or four in a TRF. Even if they are out of tune you will usually still get reception.
Shall we also talk about short wave? More switches in the band switch to get dirty.
Superheterodyne was a significant improvement over TRF in many ways.
Best Regards,
Bill Grimm