Absolutely justified. I didn't have one until my late twenties when the flat I was renting had one, I loved it. When that relationship ended, I think I cried more about leaving the dishwasher behind than the twunt man.
It takes less than 5 minutes to load and same to unload, much better than the 40 mins or more washing up.( ok some people can wash up faster, but I'm a rinser and that's how long it took me) plus you can pile all the dirty dishes in it so instantly the kitchen looks much better!
Then had to go a few more years without one, which included DS arrival. Bottles, weaning etc, not fun. When we finally managed to buy a house with a big enough kitchen (as opposed to the series of shoeboxes) my main demand request was a dishwasher. I still love it!!
Hope your hand heals well OP and yes you deserve it!!