This is where you are wrong wrong wrong. Old Poppy was unhealthy because she could ignore an entire team to kill your carry. Yorick is unhealthy because he makes being a melee more miserable than it is. Urgot is unhealthy because he only needs to land his E so he can spam Q till you die, or he dies.
Are these champs fun? Yes, to the person playing them, but they often feel unfair and unfun to play against, hence being Unhealthy.
You tell me that you could play Old Poppy Ap, As and crit and that's true. What you fail to remember is that Poppy original design has always been a Tank, but her busted ratios have always, and her busted Ult, made people stack full damage because it worked. It worked, but it was unhealthy as F**k, and unfun to play agaisnt at all.
Like said, Solo lane Soraka, just like solo lane Janna a long time ago, wasn't a widespread thing, and if it was, it was because it had an unhealthy aspect to it. Soraka will be a support, up and first most. Why take away power from her main role, to buff a less common choice role?
For Morde, I can't speak a lot about, but what i read about from Malicious Metal, a highly dedicated Morde main, he has found high success with Morde regardless of being in a solo.