Yeah, I think that's fair.
To my mind, there's a difference between "the DM's PC" and a DMPC. The first is what you describe: the DM is also a player with a character. Some groups might have trouble juggling that, but I know it works fine for others.
A DMPC, on the other hand, is something like "the DMs favoritest PC 4evar!" The character is often overpowered, and might be a recurring PC in that same setting or even in others. Adventures often end up revolving around the DMPC, too, consistently and in ways that go beyond the NPC as plot device (who does their important thing, but then leaves the spotlight).
Back in the 2e era, I played for a while in a long-running campaign with a DMPC in this sense of the term. (There were 6 players, so it wasn't necessary to fill a spot in the party or anything.) In this game, the DMPC was the object of every quest, the key figure in every storyline, a buddy of godlings and kings, and powerful beyond their stated level. While there were a couple longterm PCs who had prominent roles in the story, most of the PCs were effectively supporting cast in a grand multicosmos-spanning story about the DMPC. I mean, the story was vaguely interesting, but I mainly played just to hang out with friends; and when I left the game, I didn't miss it. Or even remember much of it.
So that's my DMPC story, and why I tend to avoid them. I imagine it largely comes down to one's personal experience dealing with them.
See, that is an example of bad DMing. That sounds fracking terrible.
OTOH, I've got 2 campaigns that I took over from another DM, and both technically have a DMPC. They level up when the party levels up, they're assumed to be with the party unless there is a reason for them not to be, they get to just be cool every once in a while, they have ongoing plot threads from when they were just regular PCs that have become more like "recurring NPC quest-lines" in how they're handled, and the PCs are free to ignore them. They don't, because this guy is one of their close friends and they like him (both of them), but they could, and they know that.
In my Eberron game, the group just basically got a quest to accompany Khalid the Shadar-Kai Monk/Rogue (Cobalt Soul/Inquisitive) to his home in Thelanis, in the shadowy kingdom of Shaelas Val, and on to the City of Night, to bring what he and the Vryloka Paladin have learned about their people's shared past and lost true homeland to The Sisters, and possibly find what they need to complete the puzzle of that lost land, and find it again.
This is a type of story/quest that I do sometimes with NPCs that aren't at all part of the party. It's "recurring NPC X"'s personal quest. There will be tie-ins for multiple PCs in different contexts, moments to shine for multiple PCs, opportunities to be the person who saves the NPC or finds what they need or forces them to face something difficult, etc.
In a fight, Khalid often takes out minor mooks, stalls a dangerous enemy at an opportune moment, provides opportunities for others, or even just serves as a vehicle to introduce a complication like enemy reinforcements arriving, by way of using his turn to narrate him doing some wild monk nonsense only to stop dead in his tracks, go "oh [curse], we got maybe half a minute before we are royally [curse word]" to announce the arrival of a new dangerous enemy or whatever. My style of running combat tends to occassionally involve huge fights that the PCs are at the hinge-point of, with most of the battle happening around them. NPC allies tend to be involved in those peripheral elements of the fight unless needed at the side of the PCs.
But Khalid is, from a roleplaying perspective, fully a member of the party. If he died, they'd be calling on Jorasco for a rez. It wouldn't work, because of his origins and who he serves, and they'd have to either perform a ritual to allow it to work or go on a 1-2 session quest to find his soul, but they'd try.
And it adds to the game, and is a useful tool in my kit. The trick is simply to not use them as a vehicle for your own aggrandizement, or to make them The Chosen One, or whatever.