The tags aren't that hard to remember, either. Do not bleach is the only one that you have to think, oh right the triangle is a bottle of bleach. The circle in a square is describing spin cycle. The circle with no square is describing drying without heat. The iron is describing an iron. The dots always represent the three levels of heat, just like on your iron.

I remember this in spite of not having done laundry in 5 years. And you're exactly right. New symbols mean little to me, I would still need to look them up and then there would be twice as many bad symbols.

This redesign article is an example of why you should avoid UI/UX people who can only design. They'll change your branding everytime they get bored and create more headache than they solve.