Until a local hospital calls you to let you know your kids got a broken leg...
And yet....... somehow we've been able to survive all this time without everyone having instant access to us.
Talk about your first world problems.
All the time "we" have been around (unless you or me are >70 yo) there have been phones. And back when there were not, hospitals were localised enough for one to have sent a runner or despatched a telegram for hand delivery to where you lived if things were life threatening. They did that sort of thing in those days.
Stop feeling guilty about the First World. Nothing to stop a runner being sent in the Third World (who largely have cell phones these days anyway).