Do SA cleansers really work?

Hi friends! I've been meaning to ask some opinions on this. A while back, I started using The Inkey List Salicylic Acid Cleanser as a step in my exfoliation routine. It has 2% salicylic acid, tolerated well on my skin (not so sure if there has been any significant changes tho, I don't pay too much attention to my skin most of the time lol), pretty affordable and accessible for me, and is a product that has been recommended by many. However, I have heard some contrasting opinions on the efficacy of salicylic acid in cleansers. Some say that having the product on your skin for at least 20 seconds is enough for the salicylic acid to work itself onto the skin, while others say that because it is a cleanser, essentially you'd be washing away the product and not allowing more time for the salicylic acid to penetrate the skin. The latter would recommend using leave on products instead (e.g. toners, serums, etc) I'm the kind of person who likes a somewhat minimal routine and feel as if I apply too many products on my skin/have too steps AFTER cleansing, that by the time I reach the last step in the routine, the final product would not be able to penetrate my skin. Also because too many steps is just tedious and complicating for me lol. Just to give you an idea, this is what my exfoliation routine looks like: SA cleanser > mandelic acid toner > serum* > moisturiser > 2 facial oils (* to be added into the routine) So, my question, do salicylic acid cleansers really work to exfoliate the skin or should I just switch to a leave on product with salicylic acid?