I'm a support main, and I deeply appreciate that I can two-trick Nami and Zyra in the same position. There are aspects to playing support which hold irrespective of champion; if you're frustrated with "non-supports" in the position, I wonder if it's because those players aren't doing what's expected of any support as opposed to the problem being their champion choices. Alternately, it could be that the players aren't playing those damage supports appropriately, but again, that's not a problem with the champs.
In the end, though, you're not going to get what you want, because Duff is right. There are times when it's simply left up to you to carry, and as strong as enchanters are right now, you will find teams who simply aren't on a level that your best game can fix. Nami has a better win rate than Zyra overall and is generally considered a stronger support, but I currently play Zyra every game because if I do well, we're going to win almost every time. It's much more of a crapshoot with Nami, because I can only heal and CC so much for teammates who play like lobotomized monkeys. I like having more control over my fate; most players do, I imagine.
If you're an ADC and you feel like you can make excellent use of a more classic support champ as a lane partner, tell your support in champ select. They may not all accede to your wishes, but some will. Some will be happy to play that type of champ, because they're like me—they only stopped because not enough teams or lane partners could make use of what they did. Just speak up.
