It's a linchpin of a question.
I usually just put it in back of the info sign and lock it with a cable lock. If you're not comfortable with it being that close to the parking lot, take it aways up the trail (minding where the Wilderness Boundary is, if there is one) and tie it to a tree, or somewhere a little more inconspicuous. If there's no trees (say Mt Bierstadt), try in back of the outhouse - the handle to get to the Good Stuff makes an alright place to tie a bike to (and who's gunna be looking back there?). Another idea if you're camping the night before is just keep your campsite up, and put the bike in your tent - or at least near it. If you can't see a the bike from the road, no one is going to go search for something that may not be there - that's not how an opportunistic theft happens.
I would say that most any TH that's not right by a main road just isn't going to have a roving band of bike thieves looking for something easy to steal. A bike thief usually needs a market and that usually means a city. Go to Silverton and see all these nice bikes just laying around. No Side by Side owning Texan wants anything to do with your silly mountain bike.
On trips where I'm out for many days, I usually pick a trailhead that has a USFS campsite with host, and ask the host if I can stash it somewhere - they're usually very accommodating.
Two tours of the 14ers, without a problem. Some trailheads do have bike lockup areas, like Longs Peak, Maroon Bells, and Fourth of July TH. I bet we'll see one at Quandary soon. Any TH that's going to have a reservation system that doesn't apply to walkups or bike-ups will have one soon is my bet.
Like leaving anything - including a car, at the trailhead, there's a risk it'll get stolen something along those lines. The world can be ugly. But I think it's a small risk. Put the bike on some sort of insurance (renter's, etc), register the serial number - heck get something like the Spot Trace (or play around with the idea of an Apple AirTag). You also don't have to use the fanciest bike in the world. I rode a steel Surly to all the 14ers - black with all the stickers taken off to de-tune the look. A $5k+ full squish rig isn't needed.