Heres my linited educational experience. In other words, I ain't no guru.
That "analog sound' is the cumulative result of every single piece of gear that the signal is run though, as well as recording method and mixing techniques.
In my own personal experience, here's something I've encountered.
I'm doing some projects where I'm taking recordings I did 20 years ago and dumping them into protools.
Some ended up sounding like crap. How could this be???? In theory the daw has an exact duplicate of what was originally recorded on a console to tape.
Why it sounded like crap was because now that I could easily edit, I did. With wild abandon. All niose, mic bleed, ect was surgically removed. Final mixes in the daw ended up sounding very clean. But incredibly sterile. The original all analog mixes had some punch and some balls.
So I redid the songs without crazy editing, just some minor fixes, and simply ran the tracks from the daw through the console.
Sounded analog again.
In short, that analog sound is a combination of many things. Some people expect to put a box at the end of the mix chain and it's going to magically transform it into that analog warmth and goodness. I think not.
Recording techniques, modern tape emulation plug ins, mixing techniques, skill and a good ear can.
Just one non-guru's opinion