I don't believe those points were too unreasonable. 2/3 are stats. And the wards... I really don't see the problem. It has zero stat bonuses. If anything, you're the one trying to ruin the game mode by being Mr. The-Glass-Is-Half-Empty.
Ever heard of ganking? Roaming? Sure, the minion wave is gonna push tower and will be a problem, but that's why you wait until the enemy laner is gone. On another note, if you're playing a champ that doesn't have good wave clear, chances are you have good poke or all-in potential. You've suggested that there is a champion who literally just sucks ass and can't do anything.
Coordinated efforts, or people will just not pick supports. Probably something I should have mentioned earlier, but it's true. People might just not pick a support. And again, Ganks? Roaming? There are some support champions/players who like to roam to secure some early kills. In case you didn't know, assists and kills reward gold. I.e. they are a source of income.
That last point, for the champions you mentioned I legitimately have nothing on it. The support thing was because the majority of people who can heal are supports. What I will say however, is that most game modes have a banning phase, and if this game mode would come to fruition these champions would be 100% ban.