High speed railways are not that expensive. I'm not talking about 700km/h but around 300km/h.

Spain has plenty of them, according to Wikipedia only China has more. And if I'm not wrong, Spain is building them in other countries too.

https://en.wikipedia.org/wiki/AVE

https://www.pbs.org/wnet/blueprintamerica/video/web-exclusiv...

I seriously question "massively profitable", especially if you do it as a private company. You'd have to buy the right-of-way, and then pay taxes on it every year. That's some pretty expensive real estate. Then, the maintenance requirements on high-speed rail are pretty stringent. That costs, too. It's not just the cost of the train crews and the electricity (or fuel) that you have to think about.

If you've got real numbers, I'd like to see them.

I was thinking a retrofit of existing rails as well as an eminent-domain type acquisition of the land.

Eminent-domain doesn't solve the cost problem. You still have to pay for extremely valuable land.

Most of the existing tracks aren't straight enough for high speed rail.

The Acela is already above 120mph where it can. The biggest problem area is actually in Connecticut, and half of that issue is Metro North's fault, not Amtrak. (The other half is that the line is legitimately too curvy to support 120mph speed in large places, but Metro North is why it struggles to hit 70mph at times).

Which makes me wonder ...

How do you secure a railway?

If trains go 600 kph, do we get a TSA circus along the length of all railtracks? Is this even feasible?

You just don't, it's not really needed.

Never underestimate the poder of idiots in large amounts.

"hundreds occupied high-speed railway tracks for around 3 hours, blocking services linking Figueres, Girona and Barcelona,"

https://www.thelocal.es/20181001/pro-independence-protesters...

A thick log or dead deer across the tracks of a high speed train could lead to catastrophe.

I once rode the Eurostar from London to Paris and as I recall all the high speed sections were enclosed in very high, barbed wire fence. So some security is definitely needed. Collision energy goes up with the square of velocity.