Washing them isn't really how that works unfortunately.

You
might eliminate any mites/lice, but what about tapeworms? Avian flu? Roundworms? Mareks? Fowl pox? Cocci strains that are lethal to either group of birds?
Of course you CAN just dump them all together if you don't mind the fact that it could kill your whole flock and leave something lethal in your soil that lives there for months or years... And quarantine doesn't eliminate that risk entirely... But it's about minimizing the risk and only you can decide how much risk you want to take. The longer you wait, the less a chance of spreading a deadly disease into your chicken pen. Some people value their birds intensely highly and will wait months to integrate. Some people have low value flocks they keep for food only and will just dump them in same-day.
Generally speaking I quarantine for 4 weeks, 28-30 days. That's pretty standard and it allows most diseases that they've maybe picked up from their old home to rear their ugly heads or at least show symptoms. Longer or shorter is up to you and your risk tolerance.