A Murder Hobo is a character who has no fixed abode (which describes a _lot_ of D&D characters) who solves all their problems by killing everything.
I have to admit that I have had very few Murder Hobo experiences. The four DMs I spent the most time playing with simply didn’t make that kind of play rewarding. Yes, they rewarded playing deeper, well-rounded characters but the fact that there would be huge (legal and likely lethal) consequences was the real reason not to go full Murder Hobo.
In some senses, a classic dungeon crawl can really end up being about being a Murder Hobo... as long as there aren’t any traps or puzzles or reasons to be sneaky. Really, dungeon crawler board games are more Murder Hobo than many RPG dungeons.
So, what’s wrong with being a Murder Hobo? Well, nothing really. As long as everyone is on board and everyone is having fun, I don’t see why there’s a problem. I can even see a longer campaign being possible, either as professional dungeon clearers or fugitives.
In fact, 3:16 Carnage Among the Stars is a game that, on the surface, is about totally being a science fiction Murder Hobo. However, at the same time, it explores the moral dimensions of being a Murder Hobo, which might make it a subversion.
Maybe I don’t understand the true nature and definition of Murder Hobo. Maybe it’s less about being homeless and killing everything and more about mindlessly treating every problem like a nail for your murder hammer.
It might not be my cup of tea but I’m not sure if I have any reason to object to Murder Hobo as a philosophy. I object to people making the entire table angry and saying ‘But it’s what my character would do’ a lot more. For me, the fundamental wrong way to play D&D or any RPG is when people aren’t having fun or at least getting some kind of fulfillment*
* Some games, like the Curse that explores breast cancer, are not meant to be fun but everyone has gotten together for a specific kind of agreed experience.