Being an assistant to the third successive United manager wouldn't sit well on Giggs' resume, IMO. Provided he has major managerial aspirations - he is at a crossroads, which could have big implications on his future. At a certain point, he has to venture out of the cocoon he's imposed on himself, or the club has imposed on him - to forge his own, independent path. You can do only so much as an assistant, and once you reach a decent level in terms of your understanding of the coaching side of the game - no amount of experience in a secondary position can compensate for the experience you've missed out as an actual manager - in terms of being the ultimate football authority at a club, managing expectations that come with the territory, putting his 'philosophy' into effect rather than adhering to someone else's, the pressure of big games and managing his personnel, and so forth.
If Mourinho is successful at United (hypothetical scenario), and is retained for the medium to long term, what exactly has Giggs gained as his assistant? And doesn't that leave him in a limbo in terms of staying on as the assistant, rather than being his own man somewhere else? And if/ when Mourinho leaves, does he have ironclad guarantees to inherit the throne, or will United do the pragmatic thing - and appoint the best man for the job with the managerial CV to back up his candidacy than a managerial novice with no real-time experience? Ryan needs a clean break. He needs to go out, and experience things from the POV of a manager, he needs to sink or swim. Sitting in the Old Trafford dugout for time immemorial would serve no purpose, unless his ambition is to insulate himself and give up on jobs elsewhere. In which case, it would ideal for the club to make it patently clear to the incumbent manager that Giggs isn't there to be groomed.
Nothing worse than the Sword of Democles hanging over Mourinho's head, and a member of his staff being after his position once he fails. Especially one who has friends on the media that can, and have put pressure on the United manager. Their intentions might be perfectly conscientious, but these things can snowball over time and cause interpersonal rifts reg. vested interests of certain individuals, and their motives (again, a matter of interpretation) - which isn't what you want at a time when the club needs to stabilize from its post-Fergie stupor.
Ryan deserves immense respect as a player, but him hanging on at Old Trafford would be akin to Gerrard being groomed by Liverpool under Klopp, and being assured of his chance when the German cocks things up - or Terry at Chelsea under Conti, and so forth. In contrast with that, Aitor Karanka had no managerial aspirations at Madrid, and wasn't being 'groomed' for the job when he worked under Mourinho. He's now building his own career at Middlesbrough. The latter's ok, the former's not, IMO.