My $.02 goes like this:

Merle Travis and some other talented folks can use the thumb method and regain position quickly enough to reach the next chord or position. There's no 'RIGHT WAY'. But, the rest of us may need the classical hand and wrist and finger position in order to move quickly. So if the full Barre F is problematic. I offer the following.

You don't have to play the whole thing at once.
I.E, if you are Travis picking you pick the notes you NEED. Or Barre the F with the emphasis on the the 3rd 4th 5th and 6th strings while muting or damping the 1st and 2nd with the first finger of the left hand to play an F chord while singing.
Rick's "five string F with the ring finger on the 5th string, etc. is great for finger picking, just practice picking up the sixth string at the 1st fret SOMETIMES to provide that bass underpining for your tune.