Actually Shinkansen/TGV/ICE run on special tracks. Passenger-only local service (e.g. BART, nyc subway) has proprietary track systems.
In the US, apart from municipal systems, essentially all the rail roads are owned by private freight companies; passenger rolling stock runs on those roads at second priority. This is true in Australia as well.
In Europe freight on, say, SNCF roads has second priority to passenger service.
When I was a kid we used to take the sleeper trains on that route but these days it's pretty much entirely freight. Most of the country stations have been shut.
Amtrak does actually own its own infrastructure.
From wikipedia: "Amtrak owns approximately 623 miles of this track and operates an additional 132 miles of track."
From the top of my head, this is the NEC (North East Corridor), some track in Michigan, and some track in New Mexico.
Ironically, their used to be a third rail line over the cascades, with was flatter and honestly, better engineered - but it was ripped up in 1978-1982 era - that is the former Milwaukee Road route thru Snoqualamie pass
In popular US corridors where real estate is at a premium, that can be significant.
In our current economy, I simply don’t see how building new trains can be economical or even efficient (frok a traveler usage of real estate perspective).
Also the right of ways are used for all sorts of things e.g. the SPRINT phone company was originally the Southern Pacific Railroad Internal Network Telecommunications
But the idea of ‘freight tracks’ vs ‘passenger tracks’ isn’t a thing in most other places.
In most of the world they’re the same thing and they prioritise using a schedule. This is another artificial problem that Americans see as an inherent one.