Telephone/cable/fiber don't generally go out as often because they won't short if they come in contact with a path to the ground. Also, power is generally at the top of the pole, so it can catch the tree limb first (for example). Then, as long as you have power for a router/modern/etc., or if it's self-powered (like copper telco lines), you're good to go.

Growing up in Portland in the 90s, I remember losing power relatively frequently. But I don't ever recall losing telephone service.