I line the bags on the checkout counter in front of what I want to go in that bag. Fresh produce go in washable bags, and fresh and processed meat go in washable, and the bags get washed when they look dirty or are smelly. I wipe out the other bags with a Clorox wipe every few weeks just because. I always wipe the cooler bag down because it gets smelly right away for some reason.
It doesn't take more than maybe 10 extra minutes a week to do all this, and unpacking the already sorted groceries is very easy and faster, and because I pack my cart in sections, it is easy to line up the checkout counter.
I timed myself today at the store. I bought $216 worth of groceries, no meat.
With my organizing my purchases into the cart as I went along, putting the bags on the counter for the following items, the cashier was beeping as fast as she could and I kept up - no loss there.
Once I got my bags into the house and Lucas taking care of the beer and a couple of housecleaning items that he requested, I got everything stashed away, including the yogurt and puddings out of their cardboards and on the fridge shelves and the bags folded wiped as needed and in the big bag, in 20 minutes. I didn't have fruit to wash or meat to repackage for the freezer this time.
I'm just saying my method works for me with no time lost for the reusable bags. Remember, it takes time to roll and stash the plastic bags for reuse, too.