Do they/we? I was born in 1983. That's probably the older end of what could be called millennial. I like thick necks and I can not lie. I associate thin necks with guitars that were made for a different era that was still active when I was really young but already starting to fade. I think OP has the generation wrong on this one but I'd expect there to be some carryover. Most of these generational terms are made up by people who need to categorize people somehow (e.g., to write articles, do news segments, or market). I think the terms are only loosely based in reality.
edit: I realize thick can be subjective to some extent. There's '59 spec necks which some people find thick and then I've tried some crazy thick almost one inch neck teles with a U shape which were pretty extreme. I think a lot of people I've met from like necks loosely based on the '59 whereas those tele necks are really at the extreme end.
I haven't really noticed that this is a generational thing, Gibson and Fender have been selling guitars with thin necks since the 60s. I suspect those of us who like chunky necks are just in the minority.
I love thin Necks and I'm not a Millenial or Gen Z. Its what I grew up with. My 66 Strat is thin. My 62 AVRI's are thin. I don't ever remember playing thick chunky neck Fenders back in the 70's or early 80's
Back in the day Chunky, big or thick necks on Fender copy guitars where considered Crappy Guitars in my experience. Its more of a last 10-20 years that the Big neck became popular I'm thinking.
As an "elder millennial" I'm used to being blamed for more or less everything, but this one is new... As others have mentioned, there's a reason Gibson refers to it as a "60's Slim Taper" vs a "People born after 1981 Slim Taper", I think.
Also, my working theory is that slimmer necks are more immediately comfortable/immediately easier to play especially for newer players. I didn't start to like fatter necks until the last year or so, and even so I think I'm still in the "medium" level of chunk. Gimme that .86-.97 range.
1983 here, not sure if that counts. Anyway, I like ergonomics. Been playing for 30 some years, and I'm honestly sick of uncomfortable guitars Thin necks are not comfortable as such for me, but if they are for someone else, I totally understand.
When I was a teenager, I used to dream of Les Paul, but now that I have a chance to buy any guitar because of being a working adult, I no longer want a guitar with "status". It can have that, but it has to be comfortable as well.
The earlier larger necks (Fender "U", LP Jrs etc.) strike me as a bit of an oversight, like someone forgot to carve the 2x4 they used to build the neck on a Friday, or they (electric guitar builders) just hadn't thought about non-body ergonomics yet (Gibson still hasn't). Very crude and primitive and "dumb" feel to those. Definitely not a fan of the slim stuff either, but everyone has their own physicality/geometry and preferences. If it were up to me, every neck would be some variation of a medium soft "V".