I'm not convinced Pep really wants Rice. I don't think he's a Pep style player, but City just don't want one of their closest rivals to get him. It was the same with Grealish. Sign him for 100m to stop any rivals signing him, then stick him on the bench for a year while you figure out what to do with him.
Clubs have always spent big on players they really wanted. However, we're now living in an era where there's a club who will break transfer records (and transfer rules) just to stop other clubs signing players. Financial doping on an industrial scale.