It's simply not possible for everything to already be there in most recordings. Surely in some classical and other acoustic music in a good hall, it can be, requiring only mixing. But for most kinds of music, a good deal of sound sculpting is done by the mix engineer (and some by the mastering engineer).
I do agree that the character (whether you consider it "destructive" or "euphonic") of analog tape (which is always there - i.e., tape has a "sound" -- it's not sonically invisible) is not always appropriate to every source, now that we have high quality digital recording capabilities. That should be a producer option - not a limitation of the studio.
It would be ideal if every studio could have both analog and digital recording systems, but given today's recording budgets, it's just not feasible for most studios to support that kind of dual system approach (or even to support just the highest quality analog approach).
Which is why I'm interested in advancements in tape emulation effects. What interests me is not the nth degree of perfection of the emulation, but the "xth" degree of enhancement to a digital souce. That is to say, with a given digital source, assuming a producer wants to present the program in a more vintage style, how well does the processor achieve that goal? Something like an ATS-1 or a high-quality tape emulation dsp allows that approach to be taken after a digital recording of the highest-possible quality has been made.
So, yes, signal quality (faithfulness to the performance) should definitely already be there before recording, but it usually isn't the naked, unadorned truth an artist or producer wants to present in an album.