I am a Zyra main, and I'll admit that I have no control over my plants and sometimes I accidentally steal kills. But with Zyra, my first priority is still vision control, because vision control is something every Support should know. If you see the enemy coming from a "mile away", you protect your carry by default.
Auto-Filled Supports are bad news for every team composition. Unless both Supports are filled, there is an automatic disparity in one very important (yet seemingly under-rated) area. If, in a 30 minute game, their Support puts down 35 wards and destroys 5, and your Support puts down 11 wards and destroys none, there shouldn't be any question in your mind as to why the other team took every dragon and always seemed to know where you were and where you were going.
This is the part that gets lost, and why auto-filled Supports are hurting so many teams. Aside from their usual "auto-tilt", they simply can not fill the role because they either don't understand it, or don't want to. In turn, as a Support Main, this hurts me, because people just don't think that anyone ever wants to Support. So they expect me to crap on them too. :/