Tube amps to play music recorded on tube microphones?

I've never made that observation.  However, it wasn't just the microphones, but the whole recording chain was tube based.  Tube recording consoles, tube compressors and EQs, tube tape recorders and tube vinyl cutting lathes.  Sometime between the early 1960s and mid 1970, nearly every major studio switched to transistors with the one exception being the continued use of tube microphones.

In the studio environment reliability and consistency are paramount factors.  Additionally physical size and heat management come into play.  What worked on a 4 track recorder won't work when scaled up to 24 tracks.  What worked on an 8 channel console won't work on a 48 channel machine.  The microphone used in the morning session has to sound the same when used for an evening session.  Engineers complained about this problem with tube microphones.

Interestingly enough, in this century tube components have made a big comeback in the studio environment.  The reason is the abandonment of analog component and their replacement by digital recording tools.  To balance the sound of digital recorders, engineers and musicians started re-using tube effects.  So they might use a tube microphone going into a digital hard drive recorder.  Or they might run the final mix down through a tube compressor or tape deck.

Actually tubes and records are better at everything. Its just you're more used to hearing modern music played back in those more common formats. So you're used to it and expect it to sound bad. When it sounds good (tubes, records) your brain gets confused. Wait? You mean to tell me its supposed to sound like this? Then how come I never hear it like this in the car, elevator, or store? 

Its like I had some nephews, made them my award winning chili. They passed and went for something out of a can. Because to them that was chili. Same for your modern music.