The hilarious part is that it's Trump's strongman wannabe dictator image that makes these things embarrassing in the first place. Had it been Obama, he could've just said "yeah, there were demonstrations outside the White House, so Secret Service turned off the lights and adviced us to go to the underground bunker. This is routine for situations like these."
I know from reading Michelle Obama's book just how seriously Secret Service takes their job, and it was a tense situation. Numerous Secret Service agents were wounded (wasn't the number 20?), and it really only takes one person getting through and then forcing a door, and you have a pretty bad situation on your hands. They take the measures they take to minimize the chance of such things happening.
So, with Bush or Obama, I imagine we wouldn't have cared. We'd have taken the lights going out, and POTUS being taken to the bunker, as a kind of illustration of just how grave the situation was.
With strongman Trump, though? When he hides in a bunker, suddenly it's humiliating. Suddenly he needs to do damage control. Which, given his child brain, amounts to "inspecting the bunker", which just made everything worse, and even more entertaining.
It's like when they couldn't find a good way for him to make it to the WWI centennial. With another president, we could easily have thought of it as POTUS sadly not being able to show because they couldn't make the neccessary security arrangements. Maybe we'd discuss whether the measures were neccessary, or if the security staff was overdoing it, but I don't know if we'd blame Obama. Bush being a "war pres'dent", who posed in military uniform and visited an aircraft carrier to make his Mission Accomplished speech, maybe, but I think I'd still be understanding.
With Trump, though, the narrative became that Trump chose not to go because it was raining. He's a fierce and fearless dictator, he can't skip something because of a bit of rain.