The rule is that flat touches up the best and usually the cheaper the flat, the better it will touch up. You will not need to touch up a washable paint as often because it will be more resistant to burnishing. It's really a choice between being a wall washer or a person that would rather touch up.

I would gladly wash my walls if I knew I could without leaving a discoloration on the wall. But I don't want a shiny look on my walls. And don't you need to go with a hint of a shine in order to get a scrubbable wall?

It depends on what you would define as 'scrubbable'. The washable flats on the market now have some degree of washability, but none are as washable as the eggshells, satins, semi-glosses, etc even though the marketing and advertising you see about them all claim that they are. If your walls take a beating and you are truly going to be washing and scrubbing them often, then yes you should probably select an eggshell which does have some sheen.