"Plenty of managers"? Maybe for smaller clubs and less pissy nations.
When Lopetegui was Spain manager, Spain fired Lopetegui overnight just for him agreeing / news leaking that he was gonna join Real Madrid AFTER the World Cup -- the competition he had already gotten Spain into.
You cannot possibly seriously think England (or United, for that matter) would be OK Tuchel doing "dual job". If anything England would probably either be at least mad at him even if he just announces his next job with us, or even if they show unexpected restrain, English media would obliterate Tuchel before he ever had a chance to step his foot in Carrington.
Spain/Lopetegui scenario is actually significant concern if we decide to hire any of the international coaches. Maybe less so for Carlo, because Brazilian FA sounds chill compared to English one and English media knows him / likes him. Dual role is definitely not a possibility for anybody we want. It would also totally undermine the interim manager and would further ruin our ability to achieve high league position this season