I play 5-string, often tuned a half-step flat, and strongly disagree that fundamental-free low notes "always" sound terrible. F'r instance I think five string sounds killer through an SVT rig, even though the sealed 8x10 cab starts rolling off above 40Hz. Psychoacoustics fills in the missing fundamental well enough.
More on topic: if you're in a nice acoustic environment, I agree that it can be nice to hear those fundamentals through Acme or other high quality bass speakers. However I usually play bar gigs in wonky acoustic environments, and my corporate/festival gigs sometimes happen on elevated/hollow stages that can have resonances with the usual undesirable results: dead notes, wolf tones. An acoustic pad like a Gramma sometimes helps, but often isn't enough. I don't have a dedicated HPF, but I use the DSM OmniCabSim, which has a Cab Size control that's an HPF that goes from 60Hz and up. The reason I got it was to "vintage up" my Bergantino CN210 cabs, but it has worked beautifully to minimize resonances in poor acoustic environments.
TL;DR: The lowest fundamentals can sound nice in the right conditions, but can really muddy things up in poor acoustic environments. An HPF can "tighten up" the low end and help the bass guitar sit better in the mix.