If you look east of the Mississippi, the overall population densities aren't really that bad, and should be able to support high speed rail easily.
...except for the fact that within metro areas, US cities are designed in a very sprawly way that's hostile to public transit. This is an entirely unforced error that has nothing to do with geography and everything to do with culture. We deliberately chose to make our cities sprawly as fuck through various regulations.
The Acela corridor is well suited for HSR. A few years ago Amtrak was trying to divest its long haul routes that lose money and reinvest in upgrading Acela, which would make it profitable. Unfortunately the plan fell through for political reasons.
Park and rides are somewhat of a stopgap measure. You really need walking/biking/bussing to rail to be effective last/first-mile options, in order for rail to be effective and popular too.
Its not perfect but that doesn't mean its the enemy of good, it can do a lot to reduce trips. Its also a drop in replacement for how a lot of people presently use their airports with long term economy parking lots, and it makes it a lot easier to justify connecting that up with more substantial transport down the line once you have that initial park and ride station.
I imagine most anywhere that would get an hsr would also have a present day bus system that can have routing better oriented to serve the new infrastructure. Bike lanes are always nice but I imagine not very many people are going to want to start their inter city trip with luggage in tow trying to lug that around on a bike.
You might be surprised. High speed rail isn't always about trips where you need a lot of luggage, and cargo bikes are popular in places with good bike infrastructure.
Of course, the number of places with actually "good" bike infrastructure isn't very high. There's the Netherlands...and that's about it. And even the Netherlands doesn't really have "great" bike infrastructure as a standard (though it does have it in some places).
...except for the fact that within metro areas, US cities are designed in a very sprawly way that's hostile to public transit. This is an entirely unforced error that has nothing to do with geography and everything to do with culture. We deliberately chose to make our cities sprawly as fuck through various regulations.