Why has the monster hunting genre not had more competition?

There has only really been three "big" games in the monster hunting genre.

1. Monster Hunter. This is at the top, and probably always be. I don't see any other studio coming close. Capcom is to the genre as what From Software is to its genre of Souls games.
2. God Eater. Quite a fun series actually, although nowhere near the quality of MonHun. Basically "anime monster hunter". It has the same art style as the Souls-like Code Vein. Some even believe it's set in the same universe.
3. Recently, KoeiTecmo made Wild Hearts, published by EA Originals. The game is honestly very very good, easily the second best of the three, but sadly poor performance and EA not believing in it sealed its fate.

There are some other minor games such as Dauntless and Toukiden (actually made by KoeiTecmo as well but never got as famous as Wild Hearts, probably due to publishing issues), but these are the "big three".

With that said, why do you think the genre has never taken off, with more actors dipping their feet into it?

Especially when we look at the live service potential of it, which we know that especially western publishers seem to love.

Monster Hunter is already a live service game, before live service was officially a thing. Well, at least kind of. New monsters were added continuously, either through updates or G-rank expansions. Events and collaborations are a thing, and the games stay active and alive for decades. Even now, Generations Ultimate is still very much active, and that game is almost 4 games old. And well, the whole idea is about killing the same monster over and over and over and over again to collect parts to build cool weapons and armour pieces.