remember that the washing machine agitates the water and the fabric to lift everything off. The soap makes the water lose it’s surface tension so it coats over everything.

historically, people would wring and slap garments over rocks or whatever and rinse them into the stream or pool. (or have concrete basins with sides meant for exactly that.) then we developed things like the washboard that let laundry be done in a tub.

so, yes. you could do laundry this way. Though, if you’re looking for specific products to help with stains… my mom always suggests rubbing Fel’s Naptha onto the stain (wet,) and then scrubbing it out. (or prepping and putting it in the laundry for not-set-stains.)