Unless you as an individual are somehow more equipped to deal with emergencies than camp staff, I'm not sure being reachable would make any difference. I would hope in a real emergency, the first call would be to the appropriate emergency service regardless.
Many summer camps require that you be available to retrieve your kid if e.g. they start showing Covid symptoms. I'd love to drop them off and forget about it, believe me.
But you can still let these people contact you, just not real-time. An hour or two delay should be perfectly acceptable. When they're on camp far away, does it really matter?
