Just finished my rewatch in time for Season 6 and I have to say, this moment is even stranger than you're letting on, because Mike did have a car. You see him drive it down toward Jimmy after the shootout. I have no idea why they didn't take Mike's car instead of Jimmy's. It doesn't make sense that Mike would want to have Jimmy arrive back in his own car for the lie, because the bullet holes give up the game. And even if that were the case, why didn't they go back for Mike's car once Jimmy's broke down. Very odd.
Another thing that didn't occur to me until just today is why didn't they bring Hector back to Mexico when he got sick? I get maybe staying in Albuquerque when he was in a coma, but once he's awake, why put him in a nursing home that he clearly finds torturous. I'm sure he has an estate like Lalo's he could live at with a live-in nurse. Anyway, he was only in the States because Tuco went to jail, right? I mean, I know the reason he's in the home is because that's where he is in Breaking Bad, but it makes no sense in the context of the show.