I have a dishwasher and it does a better job than me with the pans. It is probably more economic than I am washing up as I am generous with changing the water. It lets me get on with stuff so that I am doing other things rather than washing up while it whirrs away. Too much washing up hurts my back and when I got the dishwasher I was too ill to do any washing up.
I still do some washing up by hand, though. There are a few things that are not dishwasher safe. The microwave rice cooker is one thing and I have some sharp knives that I don't like to risk. There is also a heat change mug of DH's that when filled with something hot has a Tardis that disappears from one side and reappears on the other. Besides I only have a table top dishwasher so I usually generate a load and a half of washing up and I do most of the cutlery in the sink.
I have finally finished my stash of sponge scourers and so I am braving the reusable sponge scourers I bought ages ago from Lakeland when they were on offer. They are sort of a velvety microfibre on one side and a silvery non scratch scourer on the other. It feels very different from the naff disposable ones and it probably isn't even cost effective. I couldn't remember how much they cost as it was some time ago, but I do know I would have bought anything like that without it being on sale. On checking they are now £2.99 for four, or 75p each.
So I have a pack of four that can be washed and reused and I never need to buy another scourer, at least until these wear out. I am not sure how long they will last and you have to keep washing them which has a cost. However I do feel that even though it may not necessarily be the cheapest option when you can get 5 sponge scourers for 19p I am a lot happier with reusable than disposable.