Couple of thoughts:
Saving penalties is a different skillset than the standard skillset of being a goalie in open play. Some goalies are good at it, others aren't. De Gea has never been good at it even when he was arguably the top keeper in the world. I would not have batted an eye if Henderson had been subbed on late to take them. Probably should've but that doesn't seem very Ole.
Ole has "his guys". He's always had his guys and it's quite obvious who his 1st tier guys are and who the rest are. The first tier consists of about 15 players. Right or wrong, he's shown no ability or willingness to expand that group or change the members of that group. May as well be etched in stone. He started all his supreme first tier guys and then went with the philosophy of "these are my best players...why would I take any of them off?" Dominic Kinnear did a similar thing with the Dynamo often (and often left people wondering why he subbed so late). Not defending it. But he's definitely a "trust the talent" manager over a "play the tactics" manager. Not that he can't make impactful subs or change up his tactics. But it's limited to that core team of 15...starting a Greenwood over a Fred sort of deal. It almost doesn't matter how much talent is on the bench because once he identifies his 15, that's it.
It's hard for me to envision United challenging City year in and year out, making long runs in the CL, and winning big trophies with Ole. Not unless they absolutely nail the transfer market, spend a lot of money, and build a roster that is so strong, even compared to City, that it can overcome his shortcomings. And I don't see that happening. But Ole has a lot of good will built up. It would take a giant step back or a perfect transfer season and no incremental gain for his job to truly be in jeopardy, IMO. Don't think either of those things are likely.