It is not necessary to have 3-point shooters in order to beat zones.
It certainly makes it easier!
But if that's the answer, then most teams are in trouble.
You do have to have some players that can make a shot outside of the lane, however. If you have to depend on lay-ups only, then a zone will win. You must occasionally make a shot outside the lane in order to stretch the zone and get the ball inside. Every good zone offense will have a little bit of both - a threat from the outside and a threat from the inside.