A DM is definitely Manchester United's most urgent issue, but it would help United much more in attack and in possession-related play rather than in terms of defensive capability.
1. It would free Fred and Mctominay to do what they do best. The two of them together make one defensive midfielder and they're too shackled in a double pivot most games to apply their box to box strengths. A true DM would allow Solksjaer to free the progressive member of the pivot to bomb forward like McTominay did against Leeds and like Pogba would like to do more of when part of the pivot (which he was free to do when Matic was having a Renaissance). McFred are inefficient in a double pivot and put too much creative responsibility on Bruno, plus they both lack vision in the short pass and sometimes compel Bruno to run himself ragged to get into position to receive the ball.
2. A really good DM is a good progressive passer of the ball who can find fullback on either side and wide forwards further up rather than just passing it around the center. This again frees up the progressive member of the pivot to position higher up the pitch when the team are in possession and gives the team much more flexibility in attack. McTominay only seems to display this passing range sometimes when he has momentum behind him, which he doesn't get to accumulate as a shackled pivot.
3. Manchester United rarely get comprehensively outplayed system-wise when in Solksjaer's favored 4-2-3-1 formation because they have a zonal defense that they've been coached to implement and don't get overrun in midfield with McFred. They do, however, concede a lot of goals through individual error, losing the ball in bad areas and miscommunication. This may be a coaching deficiency or a player one, or a combination of the two, but neither would be solved with the addition of a DM. Hopefully the weaknesses would get exposed less often, which would result in less goals conceded, but a fast CB is ultimately the answer to sort out the majority of the defense's weaknesses. It would allow McGuire to play a higher line which would in turn help the midfield. It would free AWB from having to tuck in where he's lacking and instead shut down wing play and bomb forward for crosses and shots.
Personally I think a DM is the most important acquisition because I don't think anyone at United right now is going to grow into a truly great DM, but there is still a chance Tuanzebe or Mengi might become an actually reliable CB.