If Pocchettino primarily views him as a defender, then it's best for all parties that he moves on; he'll only ever be decent in that postion, but as a midfield player he is/can be very good, and a mainstay of the England team for the best part of a decade.
He'd be a real asset to United; Mourinho has a fetish for large men, and they need a proper anchor to provide a platform for the Dennis Rodman parody.
I agree that United can't take Tottenham's best players anymore; if they could, theyd gladly replace all but De Gea, Valencia and perhaps Mkhitaryan with the Spurs first 11. But Dier isn't a key player, is he? He's being shoehorned into a back 3 to accomodate Wanyama, who at 25 isn't going anywhere soon. Even Winks is probably ahead of him in his 'best' position.
With the stadium costs taken into account, Levy isn't going to sanction huge fees for upgrades or quality depth in the squad without recycling assets; for the quoted £40m, you could replace Dier with Michael Keane, a definite upgrade in a defensive context, and also cover a large chunk of the fee for a Tielmens or a Barkley. Sacrificing one quality player to acquire two would push the club closer towards success.