> time spent determining if the item is dishwasher proof

It's done once per item. In my case I have just a few things I know are not dishwasher proof.

> time spent playing dishwasher tetris

Get a bigger dishwasher.

> time spent filling and emptying

The same time you'd spend putting things in the sink and taking them out after you've washed them.

> time pre-cleaning before putting things in the dishwasher

No need to that, unless you leave actual chunks of uneaten food on your plates.

> time spent re-washing after it turns out that the dishwasher did not clean your as well as it advertised on the box

Try powdered detergent. There are a few Technology Connections videos discussing dishwashers, including how capsules are inefficient - basically they're used up on the "pre-wash" cycle. There are a few other tricks to improve the efficiency of the dishwasher, too.

So you have a few things to do once and a few things to do always, which you'd do with hand washing anyway. Having a dishwasher is a game changer. If you're not happy with the results, don't give up just yet. Think of how to improve the process, because it's possible. At first I was also skeptical and disappointed in my (first) dishwasher.