It looks like the flight in question here left at 9:11am; arrived at 10:33am in LAX. Originally should have arrived at 9:10am.

There was an 11:50 and 12:55 leaving LAX to EWR. There were 3 flights the OP could have taken from LAX to LGA. That's 5 flights that the OP could have rebooked. Either all 5 were sold out (or had a segment sold out), or other passengers took a proactive approach when initially delayed and booked themselves a later flight, just in case.

But, the OP's initial line of if "something happens and your flight is delayed, you're done for the day" is far from true. There were plenty of options. And if other airlines have plenty of options but those flights are sold out, IRROPS ain't gonna do a darn thing for them either.