I've tried the Sega Saturn version through emulation, and while it seems fairly faithful gameplay-wise, it does pale visually with missing details and 30fps framerate with some dips, although apparently that version wasn't even finished before released which might explain some things.

But unfortunately current Saturn emulators I've tried have misaligned aim the more you aim away from the center when emulating the lightgun, so it's not quite perfect, although it must definitely be good if you have a real Saturn, CRT and lightguns to not have that issue.

That said, SEGA definitely doesn't seem to have that much money on HOTD considering this was outsourced to a relatively cheap developer AND they gave them the keys to HOTD2 Remake to even worse results (it's insane how there's more issues there that make HOTD1 Remake look stellar or at least just decent to good since the animation and lightning isn't completely messed up like in HOTD2R), so I wouldn't expect something big from HOTD and SEGA unless they were to do a thing related to that "reviving old IPs" project like Crazy Taxi and Jet Set Radio.

And on that note, it would be nice if SEGA actually re-released the ORIGINAL House of the Dead one day, arcade version with all what it had, no compromises, not even need for extra modes if that's not possible, just the original arcade game as it was in the 90s. HOTD2 got a faithful port, so I don't see why a HOTD1 one shouldn't be possible (even if source code is lost, they've emulated Model 2 games before as arcade bonuses in Yakuza games).

In any case, thanks for your comment. I might have to look into some older light-gun games for curiosity sake (I'm only aware of Beast Busters because of how its sequel is exclusive to the elusive Hyper Neo Geo 64 and has seen some improvements in emulation some time ago), but for now I've been having some fun in general with SEGA's offerings.