That would work, but a large flywheel would also be a good solution. You could spin up the flywheel to store energy and if it reaches maximum speed then use the resistors. You'd also need to detect load on the grid and then run the flywheel system in reverse to assist vehicles that are moving.
Given that regenerative braking is ~60% efficient, we're talking about 1.2 kWh. That's really not that much; a typical Tesla battery pack is in the range of 65-100 kWh depending on model. Now, granted, I don't know if you can feed that much energy into a battery pack on the order of ~20 seconds, but using multiple packs would suffice.
So it does seem feasible to do it either by installing battery packs connected to the tracks, or in the cars themselves. I wonder which would be better.
There's no need for storage nor batteries at all, though. It suffices to convert the energy from the DC rails (where the train dumps it) to a bus where every other accelerating train can draw current from -- since there's lots of trains, there'll always be one willing to accept the load.
The only issue is that each third rail section is fed by its own set of independent rectifiers, and the third rail sections are not paralleled together. This means that if there's no other currently-accelerating train on the section of rail that you're on, it's just you and the rectifier substation -- and those rectifiers can't accept your regenerative braking current.
Adding inverter circuitry to the substations would introduce a path for energy flow to go from the DC third rails into the AC grid (opposite of the normal direction of flow, hence the term "reversible substation"). Since the AC grid is connected to all the rectifier substations and since there's many trains on the rail network, there'll always be a source for regenerative braking current that's dumped onto the AC bus.
The question is what's cheaper -- adding inverters to every substation, or adding battery packs on the trains? I don't know enough about the prices of things to be able to guess.
If storage makes sense (if a consumer for the electricity can't be found), battery storage (or flywheel storage) will almost certainly be kept on the wayside and not on trains; that way you don't have to care about weight / volume / heat dissipation concerns. SEPTA has such a system -- a large battery array at a station that captures regenerative braking energy.
