I would disagree on that.
Airport parking is often outrageous.
Rental cars at airports are just as bad as parking rates. Lots of extra fees.
Amtrak to international flights in most places is not reliable due to arrival lateness except in places like the NEC.
The use of Amtrak at airports, imo, is for those coming from elsewhere into the metro area (but don't need downtown access) and those who are connecting to a flight. Sure, the Amtrak LD network isn't reliable enough today to have that, but ideally they would be, and if the corridor plan takes off those are well-suited for rail-air links since they should be more reliable. The rental car prices might be higher, but at least they're on-site and usually open into the evening, on weekends, and often 24/7 or close to it. Most off-airport car rental locations are open rather limited hours (often 7/8 AM - 5/6 PM M-F, then 8/9 AM - 1 PM on Saturday with no Sunday hours.) Even the one at Union Depot in St. Paul isn't open for the 10 PM arrival for the Empire Builder, but the airport location is open and ready to give you a car.
They're also often fairly convenient to reach by car, with facilities set up for easy pick-up and drop-off as well, and many also have vendors outside of security to grab food/drinks.
If you have a car, rather than parking it at the airport to take the train, drive to another station with much cheaper or free parking. Who wants to pay as much for parking for a two week Amtrak trip as it costs for the train itself?
I'd rather see non-stop or minimal stop shuttle trains (with room for bags) between the airport and a convenient downtown Amtrak station since that will have lots of passengers who just want to go downtown.
Sure, most people who are parking will likely be better served by a more traditional suburban station. Ideally you could have a couple to do that.
As for non-stop/limited-stop shuttle trains, there's typically not enough traffic (even with general downtown ridership) to justify an exclusive rail link for that. It also throws in another connection, transferring luggage again, etc. If you're going to build a connector train from downtown to the airport, it's better to make it a standard urban-style train with stops so that you can (ideally) get a lot of additional traffic that's not just downtown-to-airport related. If nothing else, there's a lot of people that work at the airport that will utilize transit, and the train needs to cater to them as well.
IMO, it's a lot better, if the train is going to go near-ish the airport anyways, to add an airport stop or build the infrastructure to do so instead of relying on local transit. It's a lot better user experience and there are advantages to having an airport stop beyond the rail-air connection.