Players control their characters. DM's control EVERYTHING else in the game (and even when done fairly and appropriately, that control sometimes intrudes into usurping the players control of their own characters). If the DM wants to "win" - they win. If the DM wants "a character" which is controlled entirely by themselves to dominate the game and disrupt the enjoyment of the NON-DM participants (a.k.a. players) then that's going to happen whether the DM adheres to the same strictures applied to the player-characters for that DM-controlled character - or doesn't. If the DM mandates that their own "character" be a party member, party leader, party wallflower or whatever, it is all but entirely irrelevant if that character does or doesn't have the same kind of character sheet as the PLAYER characters do, or follows the same rules (more or less) as the other PC's do in character creation, earning xp and treasure, etc. If the DM has a NON-PLAYER character do the same thing nothing is different except the nomenclature.
Yes, the manner in which DM's participate in the game is different from players for whom the DM administers the game. But for persons who aren't even participants in a given game to deny a DM permission to, in the game they themselves run, have a character who more or less follows rules for the player characters (what most label as a DMPC), is not functionally different from denying that DM permission to have NON-PLAYER characters (NPC's) who fully DO NOT in any way need to conform to player character restrictions. What is happening here is lack of understanding by certain DM's why they have a separate experience from the players in the first place. There's DM's who realize that thing I mentioned before about, "If the DM wants to win - they win." Maybe not even a conscious realization. But they then use the power of the position of DM to FORCE the intended manner of participation of the other players to take a back seat while the DM takes center stage utilizing a "player character" that is run by the DM as their instrument for doing so. They can and WILL do the same thing with an NPC as they would do with a "DMPC". If anything it can be worse with an NPC because an NPC doesn't have to follow PC rules. It's probably more annoying to players when it's a "DMPC" because ostensibly the DMPC has to stick to the same rules as their own characters do, but obviously the DM then uses their own position AS DM to misuse that character to the much diminished enjoyment of players.
It's all nearly identical symptoms of the same disease. This is a DM problem in general and NOT a problem with "DMPC's" in particular. It's simply frequently seen through the symptom of DMPC's whom the unfortunate DM has disrupting their own game's enjoyment for their traditional players/participants. You can simply write a rule into the game of, "The DM MAY NOT run a player character in their own game," in red ink, all caps, and a different font, and it wouldn't change a thing. DM's and players do indeed have different avenues of participation in the game, and this is simply the DM not understanding the difference, and possibly the game rules text not making the difference sufficiently clear (but I doubt that - it's just DM's who don't yet get it, and won't even if it's written out for them.)