That’s… not really how it works. It’s nice if the DPS can do some peeling on occasion, but really, the other support should be your primary source of peeling. If your DPS are constantly hanging back to peel for the supports, then your tank is just flapping in the wind with no damage pressure to help keep them alive.
Also, it’s kind of absurd to suggest that your teammates need to earn your support by proving that they can get stuff done without it. The amount of resources they have to work with makes a huge difference in their effectiveness, and you as a support are a big part of that. (Not just in terms of direct resource donation, but also in terms of helping your tank and other support do their jobs effectively.)
You can choose to do whatever you want, of course. No one can sue you for lack of heals or anything. But if you want to perform well, you need to learn to adapt to what’s happening. If you’re letting teammates die because you’re so busy struggling to stay alive, then maybe you need to change something about how (or who) you’re playing.