There are still guitar amps (incuding high-end ones) marketed around that sound, too. Many of the DSP systems even claim to have some of that warmth to them. As you say, it may not be objectively "better", but many seek that sound.
well of course they can replicate it, the average windows ten computer has more processing power than a 90 recording studio, you can do much what you want to achieve the sound you want, even completely remix it if your so inclined
you really need an understanding of 60s and 70s recording techniques to under why they had that sound you crave
first they had rubbish mikes, they couldn't record low base say bellow 50 hzs and almost no treble about 12 khz.
second vinyl is a rubbish medium for music, they couldnt put much base on as it took up so much room and not much of the limit treble they had as it would cause all but the most expensive needles to skip, so what your left with is a slightly trebly mid range. they corrected this by designing amps ( and speakers) to put back what was missing in the original recording, ergo most of what you want is in the amp configuration and not on the record
that why classic album sound so poor through cd player and modern amp, your just getting whats on the recording, which isnt very good, unless its been remixed and then it seldom sounds like the original. the remix of hotel California is awful
a quick rejig of the setting to make it slightly blurry, lower the dynamic range to 12 bits,drop the high treble and boost the mid range base and it sounds just like the original played through an expensive tube amp, even my Samsung tablet has a @ make it sound like a tube amp@ function
all this is helped if you play it through some worn out speakers to get '' warmth'' as modern speaker are again to good for the music,