You can fix the density problem, at least on one end, with park-and-ride lots; every successful commuter / regional[3] rail service puts parking next to the suburban train stations. You just need a dense corridor for people to go to.
For people commuting from suburb to suburb you put bus connections at the train station. Buses are lower capacity but cheaper to purchase and operate so you can run a bunch of them in low density[0] for improved coverage. If demand is really bad[1] you create a "microtransit zone" - i.e. offer shuttle taxi service to the rider's final destination.
What I'm describing is basically how UTA's FrontRunner commuter rail service works; but it's not materially different from, say, the NY MTA's LIRR or MNR besides the larger scale of the NY systems and the fact that New York is weirdly bad at buses. For various reasons America has actually done decently well at retaining the commuter rail systems that worked and rebuilding the ones that got scrapped. This is primarily because these systems tend to be small-scale enough that state & local governments can fund them with their own money and the meager amount of FTA funds available.
The comment you replied to confused "rail commute" with "commuter rail"; but the grandparent was specifically talking about intercity travel. Here is where America is actually malincompetent[2] at building anything. Our primary intercity rail operator, Amtrak, was built as a last-ditch service preservation measure as railroads were bleeding money on passenger traffic. It doesn't own most of the rail it operates on, and that rail has been actively getting worse as Class I railroads have been destroying their own infrastructure (especially Union Pacific). The two-and-a-half attempts at building high-speed services in the US have all been various flavors of bad:
1. The most successful, the Acela, works primarily because Amtrak owns most of the corridor. Even then, it barely gets up to speed because "high speed[4]" (80+ mph) trains have to be grade-separated in the US, which is expensive, and the Acela was sold on the promise of incremental upgrades that haven't really panned out
2. BrightLine partnered with a freight railroad that wanted to get back into the passenger market, and it's actually operating at "higher speed[4]", but it's also bleeding money. They have a second route planned from Los Angeles to Las Vegas, but it's a project they bought out because it was... also bleeding money.
3. California wanted to build their own Acela, with blackjack and hookers, and wound up massively overselling it to voters. At least in terms of how much it would cost and how quickly it could be built. They bet the farm on FTA funds that got impounded the moment Trump retook office. I have no idea if this will ever happen.
You'll notice I never mentioned population density, and that's because it doesn't matter for intercity travel at all. The vast majority of flyers get a taxi to the airport and a rental car at their destination, and it still works out anyway. The only difference to those kinds of travelers between a train and a plane is time and whether or not they have to take their shoes off before boarding the vehicle.
[0] Or, if you're New York, you run way too many of them through medium and high density areas that really SHOULD have a subway but don't anyway build QueensLink and NO WAY WITH QUEENSWAY
[1] From a customer perspective, anything less frequent than an every 30 minutes bus probably could be served better with on-demand taxis.
[2] Malicious? Incompetent? Why not both!
[3] I am going to use "commuter rail" to refer to both commuter and regional rail systems as they are roughly the same scale. The difference comes down to scheduling patterns: commuter rail is scheduled around 9-to-5 rush hour traffic while regional rail is built to be more broadly useful.
[4] Strictly speaking, "high speed rail" means 125mph or higher and anything less is conventional speed. Rail just was already pretty fast even before Japan decided to make really fast trains.
