Hell, some things like knives and cutting boards, I clean while I'm cooking. While I'm waiting for something to finish roasting or frying, I'm already cleaning my work area. Usually, the only dishes that are left over are plates, forks, and glasses.
And it's part of the day. Brushing your teeth takes time. Taking a shower takes time. Getting dressed takes time. You have to decide that you are a person who takes time to cook, not spend 15 more minutes on Twitter.
I'm not some rural hippy who has no real job, living off of the land, disconnected from the pace of life. We live the DC metro area. And by that, I don't mean we live in a mansion in Herndon or Reston, I mean we live in an a small apartment in Alexandria. I'm the CTO of a technology consulting firm. We have only one car between my wife and me, which she drives, and I take public transit everywhere.
If you don't feel like doing the dishes every day, you can just stack them up and do them once a week...