I don’t understand the benefit of keeping them alive as they boil.
If you mean before you boil, the reason is they have a nasty bacteria in them which multiplies at a rapid pace if the lobster is allowed to die prior to cooking. Also placing them in the boiling water while still alive assures their freshness same as with clams and crabs which you also want to keep alive before cooking.
I don’t understand the benefit of keeping them alive as they boil.
As for keeping them alive until boiled, they taste better, and have been known to taste better at least as far back as the Romans - not to mention that while alive, their immune system keeps a kind of bacteria that grows on them in check, and that bacteria can cause food poisoning within an hour or so.