I am against this. I actually like finding random names in the forest. There is always the possibility that I find an awesome name, like my Zachariah for example. Actually it is much more frequent that I find good names than that I find colours in the forest, so afterall you would lose on this business. Most of the time all you would find were unnamed natties. And if you're lucky enough to find an albino, I think it isn't such a big deal to get a name tag and tag it, most albinos worth more than a name tag anyways.
But if that reason wouldn't be enough, my other reason is, that it would make name tags worthless in more ways than you think. Name tags wouldn't be necessary for the forest pets, that's just one thing. But also lets say you own the dream name "White" on a nattie pet, and you want to put it on an albino. You hatch 3000+++ eggs and manage to hatch an albino. In the current system, you would use a name tag to rename the nattie, and name your newly hatched baby the dream name. But if the forest would clear names just like that all you have to do is forest the nattie, and the name is free, no name tag needed. Also now you need two nametags to rename a pet, with the forest name clearing, you would only need one. So name tags would indeed become much less looked for.