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You're not wrong: However, that [regeneraative braking] can only work where trains are accelerating and braking at the same time, on the same electricity sub-station loop.

Or something like super capacitors to hold the braking energy until the train needs to a accelerate again

It would be much more difficult to feed power back into an AC grid from a regenerative brake. With a DC grid, no synchronization is needed.

That's not true.

1) modern railway is fully IGBT powered. In this case it is trivial to inject current.

2) with DC current you need a substation capable of converting AC to DC (easy: bridge rectifier) but also DC to AC (to given tolerances) which is much more cumbersome.