If it’s worth to purchase a dishwasher… it varies a lot given each ones own priorities and situation.
If saving X minutes a day is a big thing or a small thing… it also varies a lot given how you value your time and how much you enjoy dishwashing by hand. I know a few people who love to do it; no need to take away that joy for the sake of efficiency.
But for the vast majority, if you have a dishwasher idle, those are some minutes you get back practically* for free.
I also cook only for two, but I do it three times a day, and I have a lot to do so I value each minute saved in chores immensely. My dishwasher has been a blessing, without it I would be eating out or ordering delivery MUCH more frequently.