Most of the midwest is empty, same with other states.
You have very dense areas in the east coast, which already leverage a large train network. In the west coast, Oregon and WA already have trains connecting their largest cities (Portland/Seattle/Vancouver).
California has caltrain, and internal city trains. In the USA, for passengers, it makes much more sense to fly than trains, the infrastructure costs and time costs of trains vs planes don't make sense.
Most of the Midwest has the same functional density as Europe. Indeed, if you overlay a map of France on the Midwest, with Paris centered on Chicago, you'll find that there are cities of comparable sizes at comparable distances.
The Great Empty largely exists only on the plains and the mountainous west, where all but the most ardent fantasists concede that no passenger system is viable. But most of the population in the US lives in or near a city that would have viable high-speed rail destinations!
There certainly are stretches in the US that aren't worth covering by train, but as you say most people don't live there, and the proportion who do live there is really tiny.
A lot of the time people seem to think the end to end travel need to be viable, and ignore that if the service is regular enough, plenty of pairs of towns along the route will contribute to demand.
"You're going to have to rent a car" is a statement about historical US development patterns and political/economic decisions, not any sort of inevitable or immutable state of nature. As such, it is subject to change. It hasn't even been a century since flying around the country was an option (and for many, not even a half century), if you need a reminder that things can and do change ...
There is a separate problem that bus transit in the US is almost invariably horribly laid out, but that has more to do with the US being culturally incapable of planning transit well, and especially the US being incurious about how transit works in places where it does work. Essentially, there's a blind spot (even among transit enthusiasts, annoyingly) that assumes that transit on anything less in scale than Manhattan is infeasible, so transit planning is equated with Manhattanization where it doesn't need to be.
We already did this at least twice during the 20th century, first with invention and production of automobiles, and then again with the combined hit of the interstates and aviation.
>In the USA, for passengers, it makes much more sense to fly than trains
You don't live in the midwest I take it. It makes more sense to drive than to take a flight that passes you through one of the airline hubs for most every trip that is less than 400 miles.
The rectangle defined by Minneapolis, Milwaukee, Cleveland and Des Moines is about as densely populated as most of Europe. Ditto for a triangle like that in TX, and another polygon with one vertex in Atlanta.
The east coast train network is not "large" given the population size. It consists of a primary line (Amtrak), and very little else given the population living with (say) 200 miles of that line.
Ditto Caltrain, which compared to European service for similarly populated areas is incredibly limited. The line between Portland and Vancouver may yet see the sort of service you'd expect on that route if you were European, but it does not have it yet. The trains are relatively infrequent, and not very fast. Let's not talk about the customs/border situation either.
Rail at home:
> Boston to Buffalo: 11h32m