I agree on one part that I don't think we will see Rice Pogba pair used often except against team that sit deep. I don't know why people have issue with Pogba plays on the left. It's similar to how we used Mata on the right back in the day or how Pep used Foden/Bernardo on wing, they will operate as wide playmaker. Thus, Pogba will operate as wide playmaker while Bruno will operate more as advance playmaker.
However, just in defense of what if we sign Rice. First of all, I don't think we can sign both holding midfielder and ball player in this summer. Second, Rice is holding midfielder and we don't have that at the moment, by signing Rice we can let Fred, McTominay or may be even VDB to roam more in opposition half while Rice who is good in his positioning can cover in our own half and recycle the ball like how Liverpool use Henderson & Fabinho. Third, or may be the future plan is to play Rice & Garner in midfield two like Rodri & Gundogan partnership, and it's just coincidence that we might able to use Lingard as part of deal to sign Rice this summer.