There are good physical reasons why it needs to be per round, not per fall.
A little to the left of Bob is Carl the Slightly Luckier Hiker. Bob falls onto this ridiculous Mario Brothers sequence of ledges and warlocks. At the same time*, Carl falls from the same height, but hits nothing, and falls 500 feet in the first round.
Suppose we allow the 500-foot limit to reset for each fall, and Bob covers a total of 5000 feet in one round via successively getting blasted off ledges. What does this look like to Carl? They both jump, and suddenly Bob rockets toward the ground like Iron Man? What's propelling him?
Let's go full Galileo here and rope them together. Since Bob is separating from Carl at 4500 feet per round, he's going to break the rope almost instantly, long before reaching the first ledge.
Now Bob gets to the first ledge (while Carl is still just barely down the cliff!) and Walter the Warlock fires off an Eldritch Blast, and... misses. Well, now it's incorrect for Bob to have been going at 5000 feet per round in the first place, which means he should still be roped to Carl. So whether the rope breaks (within a fraction of a second of their jump) depends on whether the Eldritch Blast is going to hit (several seconds later).
It gets even sillier if they both hit the ledge and then Walter gets to decide which of them to blast, and whoever it is retroactively gets their falling speed increased tenfold.
Even worse than that, Walter can say "I ready an Eldritch Blast to hit the second person to land on this ledge" and now it's a true paradox, unless they both accelerate to Ludicrous Speed during the fall, which I'll admit makes as much sense as any of the rest of this scenario.
On the other hand, if we read the rule as "500 feet per round" then it's really clear narratively what's going on: Bob and Carl fell off together and they're falling together at a constant speed. If there's any interaction between them (say one of them wants to cast feather fall), the DM can simply assume they're at a fixed distance from each other for the entire fall. There's no crazy reverse causality due to invisible warlocks or hidden trampolines or anything else they might hit on the way down.
*If we're applying combat turns, then one of them is "first" in initiative order, but the difference in time is negligible. If this is hard to accept, then assume they get hit with thunderwave while on the edge of the cliff.
D&D "isn't a physics simulator" but it ain't a Roadrunner cartoon either.
This rule isn't supposed to be highly accurate (falling objects don't really have constant speed, of course). It's supposed to produce intuitively plausible results while also not requiring anyone to get out a calculator. For that purpose it's good enough.**
But allowing a creature to fall an unlimited distance in one round because it's divided into "multiple falls" isn't even intuitively plausible. Basic kinematics is intuitive for those of us playing the game--we're descended from tree-climbing apes and we instinctively know how falling works. We were throwing spears at antelope for a long time before Isaac Newton came along and explained it with math.
My point is that if you're applying this rule in a way that produces nonsensical results, then it's not achieving its purpose and you really shouldn't bother with it.
** The usual quoted values for terminal velocity of a human are 50-70 m/s, which is 1000-1400 feet per round. 500 feet per round is not a bad estimate for the first round, though, and honestly you probably don't care much beyond the first round. The question in most cases is "do I have time to cast a spell / deploy my parachute / transform into a hawk, or not?"