United needing a more defensive midfielder relative to their style and formation was much more urgent under Mourinho and Ole. But it is projecting to be a totally different approach under EtH, which requires different players, in midfield and as a team overall.
City and Liverpool play with a back 4. Chelsea, Spurs, Arsenal currently play with a back 3 and wing backs. United seemingly will play with a back 4, as they don't have proper wing backs nor enough cover at CB (considering they want to sell Jones and Bailly, and Tuanzebe's future very uncertain at United).
So a player of Rice's profile, one who doesn't venture too forward much and hasn't had to play in front of 2 CBs or with 2 other orthodox central midfielders, may not fit at United.
FdJ would be the building block of any current and future United midfield. The strengths he displayed for Ajax under EtH and for his national team, which he enjoys the best and is at his optimal level, should be complimented accordingly. And Rice wouldn't do that.