You absolutely do not have to RP this. You can say "No." You can say "Ok, you go off and do that, what's everyone else doing?"
Cover your phb in spray adhesive and leave it sitting on the table. As soon as someone touches it, shout "ROLL INITIATIVE!"
Actually, apply this to other random objects at the game table. A bag of chips, 1 can of soda in the fridge, every 3rd pencil, whatever.
Addl wisdom: some people make jokes when they're uncomfortable, as a defense mechanism. If you have a player or players constantly trying to lighten the mood, consider that the atmosphere you're trying to create may not be a good fit for your party, and/or parts of your party may not be a good fit for your game.
What's his deal?
Starbucks is a real coffee chain that exists in the real world. Moondeer and sunfawn follow the same naming scheme, but the players didn't realize that was what the DM was building to until the big reveal. It's...pun-adjacent.
Queercoding villains to make them seem dangerous and deviant to the people of the time (and those that are still stuck in that time). Admittedly, the people making that decision probably weren't conscious of that being why they thought eyeliner made him look villainous.
Peckromancer
What DM would deliberately sabotage their own game like that? No one actually wants to spend a session waiting for someone to examine an endless supply of rocks.
You select the level of abstraction for different things based on what is and isn't the most fun to delve into. If your group enjoys poking every surface with a 10 foot pole, it's not wrong to play with that level of granularity. It's just that all the interesting things you can do with a 10 foot pole are pretty mined-out after 50 years so we tend to direct our attention elsewhere.
In 3.5 at least, if you're in a space that isn't big enough for you to change size, RAW you just...don't.
I just feel bad for the loincloth mimic.
So I guess that's actually several questions, and they each have different answers.
Why does combat feature heavily in D&D? It doesn't. Or at least, not necessarily. How much or little it features is dependent on your DM.
Ok, so why has it historically been featured heavily? Because of D&D's lineage. The game evolved mechanically from wargames, where combat was the whole thing, and thematically from works like Conan the Barbarian and Tolkein, where fighting monsters featured prominently.
Why so many types of monsters, then, if works like The Hobbit only had a half dozen or so? Because The Hobbit is a single story, whereas D&D is a framework for creating lots of stories. Maybe one short campaign or a campaign arc has as many monsters as a Tolkein story, but then you go on to the next arc, the next campaign, and you need something new. You can obviously recycle lots; orc bandits are different from orc soldiers are different from orc cultists. But with (tens of?) thousands of games going on continuously, year after year, there's always a demand for new content to slot in, and monster design is often a handy thing for DMs to outsource. Hence, there are a lot of kinds of monster because there is demand for them.