"I don't have a good explanation besides why" -- this is a common "way of thinking" for people who do electronics, or auto repair. You're used to having a big "common/return" bus (often called "GND" but let's not go there today!). Either you're dealing in electronics which is very tiny current, or in automotive it's a massive steel chassis with unlimited current capacity. *So, "return" is out of sight/out of mind.
In AC mains, everything is wired as full loops - both hot and neutral are wired in every case. (for instance you would never use a steel building's structure as the neutral current return, holy smokes that would be bad!!)
However, AC power has one throwback to automotive mentality -- We do not "fuse" the neutral wire. After all, why fuse it? Since we run full loops, neutral cannot possibly have more current than its partner hot... or hots in the case of a "Multi-wire Branch Circuit".
Of course, this presumption relies on the neutral being monogamous to its partner hot(s).
What was in their head?...
I'd imagine that the above person logicks out that the L1 loads sum up to 60A and the L2 loads sum up to 40A, so neutral flow is 20A and that's within limits. This ignores the fact that not all circuits are loaded 100% all the time!
Suppose you plug in 13A loads into the three L1 circuits and a 1A TV into the one L2 circuit. You have 39A on the L1 side and 1A on the L2 side. The neutral carries 38A.
"But but but... there are 5 neutrals here with a combined ampacity of 100A. Shouldn't they be plenty to handle 60A of differential current?"
First that's "Paralleling", which has special rules... but let's wind back to "Neutrals don't have breakers". Yes, if all 5 neutrals stay intact you'd be fine... but what happens if 3 of them fail? Now you have 30A on each surviving neutral, overloading both.
Neutrals don't have breakers, so nothing would warn you of this. This is why the special rules for paralleling require individual fuses/breakers per wire, including neutral. But that opens another can of worms: What if the neutral fuse/breaker blew, but the others didn't? You'd now have a "Lost Neutral" situation - which is a nightmare. So yet another design rule requires if the neutral is breakered, it must trip the hots when it goes.
What to do
Since all these cables have their own neutrals -- they are just improperly tied together -- they simply need to be separated so that neutrals are only shared among cables that share hots.
If you mean that the white wires from 2 cables have been re-tasked to be hots, all sharing the third cable's neutral, then these 5 circuits will need to be refactored to be 3 circuits. NEC 300.3(B) requires all related circuit wires be in the same cable or conduit, This is AC -- if they are in different cables, it will induce EMF between them, eddy current heating, vibration, cracking and hotspots from the reduced conductor cross section from the cracking.
If 3 circuits is not enough, that's too darn bad. They could have supported 6 circuits with 3 cables, but they would've needed to be 12/3 cables and multi-wire branch circuits. (2 hots per neutral). I hope they enjoyed the latté they bought with the "big savings" on wire. talk about a false economy...
"Couldn't we get 4 circuits out of this by remarking 1 white to a hot, giving 4 hots 2 neutrals, and wire proper multi-wire branch circuits? Nope, 300.3(B) again.