I prefer self checkout because I get to bag my groceries the way I want. It's infuriating to line up my groceries in the correct order only for the cashier/bagger to mix them all up in my bags anyway. If I insist in bagging them myself, then I have to awkwardly do it while the cashier and the next person in line watch and wait for me to finish. At least for self-checkout, there are multiple counters and no single person waiting for me.
From your comment I assume you are American, since I heard that people pack your bags at your stores. In Germany and probably most of Europe a typical checkout process works differently and probably solves the problem.
You put your stuff on a large transport band, emptying your cart (probably have those as well)
When you're up you move your cart at the large area after the cashier
The cashier registers everything and pushes it to you into that big area
You put everything in your bags while they are working
Cashier finishes, you make your payment
You pack the last 3 items that are remaining
Some stores also introduced a simple "switch" that makes the products of the person after you slide into a seperate area, to save time .