Not really. If I don't agree to on-call, I do it on best-effort basis. That is: "Oh, I'm camping with kids without a computer. I'll try to help you as much as I can. Did you try Z after X and Y didn't work? Ok, try it and call me back how it went, I'll try to Google something in the meantime." If that would happen too often (more than 1-2x a year), I would try to improve the process or consider switching my job. And my phone is silent during the night.
I wouldn't call this a permanent on-call, just being responsive.
Also, if you can get an equivalent role with less requirements such as being on call, then I guess it is just a question of grabbing it!