A vanilla vigilance fleet packed with pilums will do the same, massed missiles scale exponentially, but at least most missiles run out of fuel or ammo quickly, lrm missiles do not.
This is it exactly, pure simple logic, tried and tested many times. It matters not the specific special mechanics an LRM has if any... Massed LRMs are hilariously broken.
Having played extensively with a Pilum based fleet, I think you're wrong. Pilums are strong, perhaps too strong, but they are not "hilariously broken".
In vanilla, an equal sized, normal fleet can fight a Pilum-based fleet; a bit of flak and it easily has the upper hand. The three double flaks of an AI Elite Onslaught can hold off the Pilum launchers of 6 Vigilances or 2 Dominators (the most you can get with the same deployment cost as an Onslaught [actually 28 vs. 30]) pretty much indefinitely. An AI Elite Paragon can shield tank them with ease as well (although it's not as good at it as it could be).
Take a pair of AI Support Dominators against each other and see how their two single flaks are easily able to hold off all the Pilums they can throw at each other. The one or two that might get through are easily stopped on their shields.
(Actually I'm playing with
Zibywan's Pilums, which are harder to intercept than current vanilla ones.)
The reason Pilums seems so ridiculously strong in normal play is because players avoid even fights. To paraphrase what someone said about my fleet: when you're throwing that many ships around, it doesn't really matter what you're using.