It's also a geographic, real-estate, and political problem. There's not enough density in enough areas with enough last-mile coverage for trains to work like other countries.
Many cities solve this chicken and egg problem by building the necessary density next to the train station. Hong Kong and Japan are the most famous examples, but it works in Singapore and large chunks of Europe as well (although Parisian banlieues may not be the best model of urban planning for other reasons...).
That falls under "political" problem. Who's going to build it? Who's paying for it? Where are they getting the land? Is it existing rail lines or new ones?
The obstacles are known, they need to be overcome, and that's very difficult in the 3rd-biggest country by population and land area with an incredibly diverse set of national and regional governance and cultures.
I have no idea why you think it has to be “twice as good” or what all that even means.
With that behind us, nobody’s proposing high speed rail from San Diego to Boston, just LA to SF and along the eastern corridor. And we can’t event have that. Let’s start small.
I don't know the full list of requirements, but a route has been chosen, some number of federal approvals have been granted, some regulatory hurdles passed, and supposedly two federal approvals remain.
The route is easier (engineering and cost-wise), due to geography, than the California rail, or anything in the Eastern corridor, and to keep it even easier they're running it along existing utility corridors where possible to further reduce the amount of private land access they have to contend with:
It means that unless the trains are moving at 400mph with perfect comfort, free wifi, and a price of $20, nobody cares.
LA to SF is a 1 hour flight as cheap as $50, with the same last-mile effort and total trip time as a train. Airlines are also elastic to meet demand without major capex.
So who's going to spend the 100s of billions to buy the land and build a line for a 2-3x slower travel option that will take a century to be paid back? California is actually trying to do this and has failed miserably because the land and infrastructure costs alone make the project infeasible.
LA to SF isn't a 1 hour flight. LA to SF is: you start at downtown SF, 45 minutes later you arrive an hour early at SFO for your 1 hour 30 minute block-time flight to LA where you then take a 45 minute taxi ride to your final destination.
That's a total of 3.75 hours end to end, assuming no fog hits you at SFO, as it does on the regular. That's within spitting distance of a rail link that allow you to jump off anywhere along the way. It's by no means 2-3X slower if you take into account the entire process, with no TSA, starting at your origin and ending at your actual destination.
For instance Ottawa to Montreal is a "17 minute flight" that takes an hour of block time, and an hour on either end, for a total of 3h, or you could take the 1h 30m train ride along standard-speed rail for $20 USD. Trains can easily be faster taking into account externalities, and much more pleasant.
They usually do in fact have free wifi, better comfort, and a $20 price point -- specifically because as you point out, they're competing against air travel.
Hundred of billions is again a weird, defeatist argument. California has failed because infrastructure in America is not about building infrastructure, it's about graft, and if infrastructure gets built along the way, that's fine too. That's the saddest part, honestly.
Honestly, this is kind of the textbook example of defeatism.
There are some odd outliers such as Salt Lake City, which has pretty low density, but the transit system is well used. It's far from universal service but in the areas it serves, it is rather popular with a wide cross section of the population.