Does a druid's wild growth put a HoT on those who are fully healed?
Yes, but only if there's nobody in range who actually needs to be healed.

In a raid environment, you can actually launch it on somebody who's just in range, and it will jump to people who are out of range. That's pretty handy after an Omen of Clarity proc on Vezax with careless ranged DPSers who bunch up too close to each other

why did they nerf wild growth and put it on a cooldown?
Because it made group healing far too easy. In the same patch, they nerfed the Holy Priest's instant AoE heal in the same way, although that subsequently got a 20% effectiveness boost.