Interesting issue - and one that is definitely very personal with no single correct answer for everyone. I grew up without a dishwasher until 1975. So my mother had to do dishes three times a day and when there was a holiday dinner, that was another production altogether. I can see both sides - when I am alone I don't use many dishes so it makes sense to keep up daily by doing them by hand. Right now, though, I have my sister living with me. She is a first class slob who believes every drink of water and every snack needs a new dish or glass- and not paper or plastic. Also, since she has limited mobility I'm the one doing the dishes after every meal, not to mention cleaning up after her constantly, shopping and preparing all meals. So for now, it's the dishwasher.
For larger groups (dinner parties, holidays, etc..) it's definitely the dishwasher. I'm not a big fan of washing tons of water and wine glasses by hand and that's where the dishwasher excels. Glasses are hard to get perfect by hand...
By contrast, one of my friends (a self professed genius, engineer and OCD) has never used a dishwasher. He claims to have "invented" a foolproof process that results in dishes as clean as a dishwasher gets them, using much less water and in a fraction of the time. That would normally be fine but he uses his platform to "dishwasher shame" his friends into hand washing and his results don't pan out. On several occasions I have had to eject him from my kitchen during a group dinner for starting to unload the dishwasher and wash things by hand. And his "foolproof" process is only correct on two counts - speed and water saving. As OCD as he is about everything (his house and yard are immaculate), I have never had dinner at his house where I didn't need to wash a glass before using it. When I point it out to him, I am being a "drama queen". Sorry, but I refuse to drink from a glass with someone else's lip prints on it.
So while there is no one correct answer for all, my only non negotiable is immaculate drink ware...