What type of refrigerant line insulation you have installed?
Typical black / dark grey foam tubing that slides over the AC copper refrigerant line (they have solid tubing and one with a slot along its length) doesn’t absorb water (unless it’s heavily deteriorated).
If you get the right size / diameter (it comes in sizes designed for different thickness of the copper tubing) the condensation should be kept at minimum or nothing at all. There might be some water dripping along the open end but not through the insulation surface.
It seams like you just have a wrong type of refrigerant insulation installed and since there’s a lot of condensation it is simply not performing properly. The AC system will still get you the temperature you need but it needs to work longer to get there.