I agree.
The names are not at all intuitive and I usually have to resort to "the purple chest does" kind of explanations when telling a friend about the logistic network.
Requester and Storage are fine.
Red could keep the Provider name.

Purple should get a name that reflects the logistic system's ...

But not all of these trees are dead. Some might recover.
I did a steam engine switch just like you did, too- does your setup also allow the accumulators to charge up to 50% before switching the engines off again? Mine additionally severs all accumulators and solar panels from the main network to ...

So recently I've noticed that the trees around my base were dying. I first thought that I'm just imagining it, but as my suspicions grew, I checked the factorio wiki and found that this has indeed been a feature for a long time.
0.12.0:
Trees degenerate slowly when exposed to pollution at high ...