I was scheduled to fly IAH-LAX-SYD yesterday on AA. Due to terrible storms the inbound aircraft (DFW-IAH) was delayed, followed by our plane being delayed. The crew then timed out. We were deboarded while a reserve crew came in. Arrived LAX at ~4am, missing my original scheduled departure of AA73. AA rebooked me on the flight today (5/8) resulting in a lost day/overnight.

HOWEVER.... AA73 was also delayed due to MX and then crew issues and rescheduled to 10:30 AM today. On landing in LAX, I inquired if I could be put on the delayed AA73 (my original flight), thus arriving 12 hours late, not 24. I was told since it was a RON/return to gate, this was not possible. Is this true?

I've certainly never heard if that either, possibly at the time if the flight had already "departed" in the system then I could see an agent being locked out of it, maybe? Or maybe the agent you were dealing with at 4am in LAX had no idea or didn't want to mess with it. Who knows.

I had an instance last year on RDU-LAX, flight fully boarded, then cancelled due to MX, everyone off, rebooked to next day, I go home. Happen to check the app and see original flight now shows as delayed, not cancelled. I book it back to airport, run to gate, and get rebooked back on the original flight now departing in 20 mins.

In any event I would certainly HUCA this morning and/or go to LAX early and try several different agents (check-in, lounge, gate, etc) to get back on the original flight.

It looks like AA73 on the 7th May wasn't just delayed , but actually departed at 23:19 but returned back to the gate , so can understand why an agent would not be able to book a passenger onto the flight after the diversion

yes. It pushed back and returned a few mins later due to MX and then the pilots timed out, resulting in the delay.

flight went out almost full.

A front line agent would not have been able to book a passenger onto a flight that has already pushed (even if it has diverted back to its original gate). But, a supervisor ought to be able to make the appropriate calls to get this done.

Often the case that, "I can;t do this" does not mean that someone can't.