My Southern Ontario home was built in the 50's at the time of lat and plaster. there is no insulation in any of the walls of the old part of the house. If the bathroom is getting renovated would it be a waste of insulation to just insulate that part of the wall?

I am getting told it that is a waste and it just doesn't make sense to me.
whenever my dad had the opportuntiy to get insultation anywhere he did it and that drafty old house wwe use to live in was eventually warm.