I disagree. There are different kinds of ambition and signing for City is really just the easier option on the scale of ambition. Ambition isn’t just taking the easy option of just signing for a team that already wins titles.
If Rice wants to and does sign for Arsenal, his ambition is there in the form of him thinking that he’s the player who can make Arsenal a title winning team. There’ll be a drive there for him to make the difference.
Same with City’s signing of the likes of Gareth Barry; he could have taken the easy option signed for United or Chelsea, he was good enough to play for anyone, but all those early takeover signings chose City to be the players that pushed us on to win titles we’d been missing for so long.
I can’t stand Arsenal, but I won’t begrudge or belittle Rice’s choice if he wants to sign for them.