Not saying that you shouldn't keg, or that it's not validly a time-saver, but there is an easier solution to at least part of this problem: Don't let your bottles get stinky and bug-filled in the first place. It will make bottling day much happier, without the expense of a keg system.
Do you store your dishes dirty and wash only as many dishes as you need, before eating? No, then your cupboards would get stinky and full of bugs.
Just as you wash the dirty dishes after eating, even if you don't need any clean ones right this minute (at least I hope you do), you should rinse the beer bottles after you empty them, not when you're getting ready to fill them. There's no grease and nothing cooked on to the bottles, so it's easy - a quick rinse with water, put them in the drying rack to drain, and you're done.
Having done that, the only washing I do on bottling day is another quick rinse to get rid of any small amount of dust that might have settled in them. I don't even use any sanitizer (homebrew purists may recoil in horror at that).