I wouldn't bother trying to make DMPCs work, there is always a better fix than the DM inserting them self as a "player." There are numerous reasons why DMPCs do not work and not many that could make them work, so why do something that basically never works when you can do something that does work.
Does the party struggle in combat? make it easier, select easier creatures or give them magic items which help cover the gap, no healer? Give them a magic item which is a flask that refills every hour with a potion of healing? Not doing enough damage, toss em a +1 weapon or something like a flaming weapon... make the party good enough.
Party lacking a face in social/RP? Perhaps nobody in the party wants to focus on that and so don't try and force it as much, go for the exploration or combat more. If it's not what you're looking for then it's not the right party to DM and it's okay to admit that. So if you're DMing a DMPC to be a party face, that is the DM talking to the DM for anything social, I can guarantee the party won't enjoy that, you might as well go write a book at that point.
But the main reason DMPCs pop up is DMs that want to self-insert their own ego, and that type of DM usually doesn't have the cognitive ability to judge how they overpower or favour their own character over the rest of the party... suddenly everybody in the party struggles to do anything and DMPC has to come to the rescue, it's not enjoyable and goes back to writing a dang book.
Whatever reason somebody can come up with to 'justify' a DMPC for, there is always a better solution that doesn't involve a DMPC and it's too easy for DMPCs to overshadow the party or just ruin the experience for the party, a good DM should be making each player/character interact with the game and a DMPC does the opposite of that, it takes time away from the players to focus more on the DM, and that is why a DMPC will never be a good idea or solution.
I wouldn't bother trying to make DMPCs work, there is always a better fix than the DM inserting them self as a "player." There are numerous reasons why DMPCs do not work and not many that could make them work, so why do something that basically never works when you can do something that does work.
Does the party struggle in combat? make it easier, select easier creatures or give them magic items which help cover the gap, no healer? Give them a magic item which is a flask that refills every hour with a potion of healing? Not doing enough damage, toss em a +1 weapon or something like a flaming weapon... make the party good enough.
Party lacking a face in social/RP? Perhaps nobody in the party wants to focus on that and so don't try and force it as much, go for the exploration or combat more. If it's not what you're looking for then it's not the right party to DM and it's okay to admit that. So if you're DMing a DMPC to be a party face, that is the DM talking to the DM for anything social, I can guarantee the party won't enjoy that, you might as well go write a book at that point.
But the main reason DMPCs pop up is DMs that want to self-insert their own ego, and that type of DM usually doesn't have the cognitive ability to judge how they overpower or favour their own character over the rest of the party... suddenly everybody in the party struggles to do anything and DMPC has to come to the rescue, it's not enjoyable and goes back to writing a dang book.
Whatever reason somebody can come up with to 'justify' a DMPC for, there is always a better solution that doesn't involve a DMPC and it's too easy for DMPCs to overshadow the party or just ruin the experience for the party, a good DM should be making each player/character interact with the game and a DMPC does the opposite of that, it takes time away from the players to focus more on the DM, and that is why a DMPC will never be a good idea or solution.