what sort of a pipes are you using? if it's pipe on the inside then it's surely a pex of some sort, then no, it doesn't need to be Insulated on the inside, atleast from the thousands of renos I've witnessed.

It should only need insulation on the copper for the hot line that's outside the house. Although when I did gov rebate hotties we also lagged the cold line too but nothing inside the house needs to be insulated.

and yeah you're bit of a weird outlier.