I'm a big fans of a headcanon that Alder and Ghetsis knew each other in the past. I don't know if they were acquaintances, friends or rivals, I just want to imagine them having their shared moments.
And in Masters EX N wonders what Ghetsis's past was like and mentions he doesn't know anything about the man's childhood.
So I like to think N once mentions the same to Alder and he starts bombarding the kid with dozens of silly and funny stories that involve Ghetsis. Something like: "Once Ghetsis was so mad after loosing a battle he tripped on the grass and rolled down the hill like a whirlipede. I was howling with laughter so hard I couldn't breathe, but then I had to carry him for 2 miles to the nearest hospital because he broke his ankle."
Ghetsis finds those memories humiliating (well, everything that even slightly hits his pride is humiliating to him) and he cringes every time he remembers those moments.
I love it too! My way of seeing it is like... older people, you only see them as they are in the middle stage or later stages of their lives, like when we see alder and ghetsis in BW and onward.
But they've lived whole lives before that. Childhood, young adulthood, even middling adulthood.. like alder had a whole family and journey before he ever became champion. You only ever hear glimpses of it but you can still sense that his life before was immense. (Just goes to show how there's a whole existence in every single person)
And as much as ghetsis and alder are opposites and adversaries, when you get older there are less people who see you like a peer and more like someone on a pedestal. (Which is a good thing for ghetsis, worse for alder...)
Which means that all of the people who are 60+ in Unova can relate to one another and have firsthand memories of another time. The idea of them, even if they didn't know each other directly (which, for ghetsis alder and drayden I like to imagine they did,) remembering points in time and big events that happened and how unova /was/ is enough to bind them in a human way. Not as just "a grandfather" but "someone who ended up as a grandfather"
Anyway, yes, I love alder and ghetsis having known each other at some point. And tying into the idea of those embarrassing moments you mention: I really like it because alders like the last line unmistakably connecting ghetsis to when he was "human". And if N ever wanted to know more about him, alder would be basically the only (non-oc non-brainwashed-Sage) person to tell him. Fits in just fine with alder being a teacher too. Win win