I find the biggest hypocritical element DMs who champion limitations as a vessel of creativity make is that they often find reasons to limit what players can play, but so not likewise limit what they can use as far as monsters and magic. Lots of DMs find it perfectly acceptable to ban the race section from Monsters of the Multiverse but then don't likewise ban themselves from using the Monster section of the same book.
Show me the DM who says they will only use the monsters from the Monster Manuel and nothing else and I'll show you a DM who actually values limitations as creativity. Anything else is "Limits for Thee, but not for Me!"
If a DM wants to run a strongly themed campaign that restricts or bans some of the familiar PC options, I would expect that they would offer some other options unique to that setting. Using monsters appropriate to that theme seems like a natural next step.
I am interested in running campaigns with a strong flavor derived from history and mythology, using ideas from 1E Legends & Lore, the 2E green historical splatbooks, and so on. I would probably restrict or discourage some options that do not fit the setting while offering plenty of others instead, and I would definitely use monsters that supported that setting flavor over ones that distracted from it.
For instance, sometime I would like to run a game based on ancient civilizations - Egyptian, Greek, Mesopotamian, etc. I have the 5E Theros book and the Southlands books for the Kobold Press Midgard setting, and if I add in stuff from the 2E green splatbooks there should be plenty of player options. The Southlands books include things like gnolls and cat people, and if someone ever wanted to play a satyr bard who plays the pan pipes, well here is the perfect opportunity. Obviously it would take some homebrew work to make it all fit together, but that is part of the fun.
D&D has had monsters based on the lore of ancient civilizations ever since the white box era, and I would definitely use those creatures (sphinxes, griffons, pegasi, etc) instead of those from other cultures, or the unique D&D monsters like beholders and umber hulks. If celestial beings show up they might be lamassu or shedu, but probably not couatl or kirin. Powerful undead would be mummies or other tomb dwellers, not Transylvanian vampires.
I am also interested in running a “Northlands” campaign, and KP will be publishing a setting book by that name. It would have an early medieval flavor with Celtic, Norse, Baltic/Slavic, and Finnic influences. The classic D&D “Tolkien races” would make perfect sense there, since that is where JRRT got so many of his ideas (including dwarf names) in the first place. IIRC the KP Midgard setting has both ravenfolk and bearfolk.
On the other hand I can also see the fun in running an old school gonzo campaign that has lots of disparate elements, like European knights going dungeon delving with samurai and witches. I would only try to run a strongly themed campaign if I could get significant player buy-in right from the start.