Insulation that looks nice?

Hello!

I have an exterior wall that has some hallway closets built in. When you open the closets you can feel a draft like the wall isn't super well insulated.

The closet is very well designed and looks really nice when you open it. I wanted to insert some insulation that I could just adhere to the wall, but I'd like it to look nice so when you open the large hallway closet it doesn't look like exposed insluation, etc.

Does anyone know of any insulation that can adhere to an existing wall and looks nice?

I've seen a bunch of sound-proofing foam/wood products that look nice but I'm unsure if any of them would add any insulating effects.

Is this a dumb idea? Can you adhere insulation on the interior of the home without opening up the walls to add it inside?