No gnu, I understand why you bought a Honda generator. My question was why the Honda generator has to have a Honda battery.
If your battery made a lot of noise, you'd have a problem with any brand of generator, I'd think, since the only noise they usually make is a sort of gugle while they vent the hydrogen and the flash-bang when it goes off.
The "Remote Start" is possibly a reason why the battery runs down when the generator doesn't run, since there has to be enough "life" always turned on to answer when the remote calls for a start.
In most areas, an "isolator" is mandatory for anything wired into the house (and should be required everywhere), and most of them also require a separate "keep alive" voltage with some drain, and may have been wired off the generator battery. The isolation relay needs to switch before the generator starts, but after the mains go down, because if it was an outside short that killed the mains - or something shorted when the ice took the line down - it might also blow the generator before the relay powers up and flips. (The isolator, assuming you have one, might not be Honda? "House equipment" makers like CH et.al. make a lot of them.)