Depends where you are of course. I used to ride Amtrak a lot between Orlando and Miami. In neither city is the station particularly convenient to downtown, especially in Miami.
Or just skip the mountain biking and take the train out and bike the silver comet all the way back home.
But! Amtrak won't let you take your bike off the train at Anniston. You have to go all the way to new orleans. It's really dumb and frustrating.
With some chatting up of the staff/conductor before you reach your actual desired premature destination, it's not uncommon for them to be cooperative on getting the bike out of the luggage car and into one of the entrances near the other carry-on luggage for you to get off prematurely with it.
But you have to talk to them early enough in the ride but not so early that they've been replaced, and it probably won't work out if the train is packed and they're understaffed or otherwise super busy.
On my aforementioned Zephyr trip the conductor offered to let me off with the checked bike @ Colfax when he learned I had a bike and SAC ticket intending to ride to Pollock Pines.
They're entirely capable of getting you off with the bike prematurely at any stop, you just gotta talk to them and give them enough advance notice. Agreed that it's annoying Amtrak can't officially offer it for all stops...
There's something magical about getting off the train in a different state with your bicycle ready to go no worse for wear. Especially at smaller stations, where the conductor or luggage handler will directly hand you the bicycle from the luggage car. It's just such a personal and practical experience compared to flying.
This fall I rode the Zephyr from CHI to SAC with my Ibis Mojo checked, with just a backpack and helmet. The conductor handed me my bike at the luggage car in SAC, and I immediately pedaled right out the station, through town, and along the American River for a beautiful day of riding east into the Sierra Nevada towards my friends' home in Pollock Pines. No TSA, no implications of being some kind of terrorist or criminal, it was rather incredible by today's standards... especially considering it cost me like $120 for the ticket+checked bike.
Edit: I also just wanted to remind folks that train stations have the luxury of residing smack dab in city centers. Good luck de-planing with a bicycle directly into an urban center. On a train it's basically the default.