Wouldn’t it be better to insulate my home?

No, insulation does not solve damp problems. On the contrary, when more moisture is coming in than can be disposed of, the insulation too will eventually get filled with moisture. Too much insulation will also block the breathing effect of a wall and might cause condensation. Initially the wall will be able to retain more heat because of the insulation, but after a while the insulation too will fill with moisture because of condensation. The insulation will not have the intended effect.