it makes no difference to us what happened in recording we can't change that. We start with the finished product and try not to wreck it too much from that point on.You don't think compression applied in mastering is distortion? "Signal integrity" is a complete joke at every level of the recording chain. We can have it in the electronics of the playback chain (dac, amp, etc), agreed on that, but then speakers throw all that integrity out the window.
Not sure what you mean about recordings being made using speakers, that's quite unusual in the literal sense. There were (and are) some amazing analogue effects systems at the great studios of the 50s-70s, including one which used a speaker in a large chamber with a mic at the other end. Some highly praised "audiophile" recordings went through that reverb system. See the Apple TV documentary by Mark Ronson for details.
High fidelity means fidelity to the recording, not some event in a studio or even a live performance. A mic doesn't hear like people nor is it in the same place as some notional person present at the recording. I mic up drums and put a mic six inches over the ride cymbal - no-one will ever listen to a ride cymbal from that position.