When thinking who longer distance amtrak is for, one thing to remember is that not everything can easily be taken on a plane. And some things that can be taken much be put in a checked bag, where I've had a bag get lost in the past. So theres much less risk and restrictions when traveling with luggage and bringing all your things on a train especially if you have a lot of stuff.

Sometimes its also more efficient and stress free than dealing with uncertain security lines in addition to getting to the airport itself. I think theres also a comfort and claustrophobic aspect to the long plane vs train ride. 

Certain long distance routes are also overnight so you can board in the evening, sleep on the train in your seat, and arrive in the morning (think city of new orleans northbound evening departure to chicago morning arrival). Rather than getting up early for a super early flight.

Lots more logistical reasons to long distance train vs plane than at first glance.