First, and foremost - EVERYTHING matters.
By reducing the rotational speed of the disc by 2x, you double the amount of time that the cutterhead has to remove the material. Consequently, there is an inherent increase in cutting accuracy. When a stylus traces the same groove, it is more often exactly where it should be to reproduce the given frequency/sound - again, more accurate.
This principle applies to the entire recorded spectrum - highs, mids, and lows. In the attached article (below), an Abbey Road recording engineer states that cutting at half-speed is 'mind-numbingly dull ', but the process results in a much better sounding LP. (> @bdp24 - perhaps Bernie Grundman has concluded the boredom is not worth the time it takes for the improvement in SQ ;-).
That being said, if a crappy recording (say, compressed, dull microphone, cheap wires) is re-cut at half-speed, you may be disappointed in the result. Remember, EVERYTHING matters. I have both fantastic -sounding and crappy-sounding half-speed LPs.
Yes, there are many other techniques to improve LP SQ, including direct-to-disc, 45 rpm, better quality vinyl, etc. and each can be independently employed. In theory, you could have a half-speed mastered LP, pressed on uber-vinyl, that plays at 45-rpm.
Regarding the digital vs. analogue issue, I find the transducer plays a prominent role in the SQ.
For example: I have the same recording in both formats - simultaneously recorded on Analogue tape and Digital tape. I find a very good TT cartridge (my Hanna ML) can transform the soundwave-medium (mechanical to electronic) better than an average CD player (my OPPO, digital to electronic). Consequently, the LP sounds better than the CD every time I compare the two. (of course, I am also hearing differences in tape-heads, etc.)
As an aside, my main system has a pretty good CD player as well (Ayre), and the SQ is closer to that of the LP.
Now the aforementioned link (begin reading at "What exactly is half-speed mastering?"
All You Need To Know about Half Speed Mastering | uDiscover (udiscovermusic.com)
Best,