The reasoning behind /MY/ dislike towards 'those' champions
First of all, no, I really don't think any of these champions are overpowered. I like to use the word overloaded, instead.
THOSE Champions:

It's because they have SO much in their kit that they can do so much with it, regardless of just about anything, really. It's either that or they lack something that is usually barring to other laners, like mana or energy - when a champion lacks both a simple kit AND lacks resources to bar them from being strong, I seriously want to just dome myself when VS'ing these champions. It feels like you're out of control when you VS them because they just have so much more to do than you as a champion that otherwise lacks the benefits of being from a 'different generation'.
VS
? DASH-HASAGI-AA-DASH See you later motherfucker, see you when my shields back up Kay?
VS
? She doesn't need to worry about resources and can constantly dash around - absorbing damage and stunning you consistently.
INSERT SUPPORT NAMEPLATE HERE
VS
? The guy has so much in his kit that you could make 2 champions out of it. This guy is a MAJOR pet peeve of mine, seriously, either give all supports this much utility or consider revoking some of his. This guy SERIOUSLY doesn't need more shit than Nami, Janna and Sona combined.
You get the point. It's kind of like walking into a gun fight with a knife - the person has SO much more say in what's gonna happen than the dude with the knife. The guy with the gun - HE WILL - be able to walk around you, point it at you and don't you fucking dare get near him kay? Because the second you do you're gonna get gunned down like the degenerate that you are. Sucks to suck - don't worry you can just pick up the leftovers of the economy and just hope that something better is going to happen in the future.
I'd like to believe that each and every champion should have around similar amounts of capabilities, what if supports had as much utility as Yasuo did dashes, shields, crit, built in knock ups, spinning HASAGI variant, windwall, hybrid damage
5 Years later
Armor penetration, reducing his Q cooldown by attack speed - - - yeah, you get the point. So why not equalize the playing field? Hell, I'd even sacrifice damage on supports for more abilities or things to do!