If they get rid of him, or nerf him to obscurity, a new 'toxic, broken, unfun' champ will be thrown into the spotlight.
Like you said, before, it was Soraka/Shaco/Heimer/Shen. They were nerfed a long time ago and have since faded into obscurity (except Shen who was semi-recently buffed). Most people playing now weren't even playing when they were ridiculous and don't know of the horrors they inflicted on soloqueue.
Atm, those so-called unfun champs are Darius/Diana/Teemo/Katarina, and Blitz, like you mentioned.
Tone down Blitz, then these 4 get complained about nonstop. After they get pruned, it'll just be a new breed of extremely obnoxious champs.
It's always going to be there - and it could be much, much worse than Blitzcrank. Considering all the 'annoying' champs that have ever existed in this game, pre-rework Eve, release Xin/LB, release Vayne/Irelia, spellvamp stacking Vlad/Akali, Blitz is tame in his damage to the game. He's not completely unkillable, he's not completely unmovable from lane, he doesn't 1v5 without taking a scratch of damage, and he doesn't force every single person on the map to towerhug the second he runs into the fog of war. As irritating as Blitz can be you CAN outplay him, unlike old Vlad/Irelia/Xin, who just rolled their face on the keyboard, won 1v3s with ease, and never, ever died.
If I had to lane against Blitz or a pre-nerf Heimerdinger, I'd take the blitz any day of the week.