I've been on-call for decades and 24x7 caregiver and it's not an issue, even in emergencies:

1. For non-emergencies, just use social media or email, which have better anti-spam filtration.

2. For most true emergencies, "hang up and call 911" just like every doctor's office recording says.

3. For urgent non-emergencies, either accept the consequences of waiting until your can reach the person via option #1 above, or get creative. Contact friends of the person and ask if they can get ahold of them... or someone IRL near them to get their real-world attention.

4. Consider what happens if you lose or break your phone. Responsible people let a reasonable group of people know how to reach them, and the rest contact a member of that group.