Well, if you invest 10-20x that much in your coffee machine, you get something that's much less of a maintenance hassle and makes significantly better coffee. Worth it if you drink coffee every day.
Honestly, it's all about the beans. I've had fantastic coffee from a $20 french press and horrible coffee from a $5k machine. Don't splurge on the machine, splurge on the coffee.
Admittedly, I'm not a coffee drinker, but rather a tea drinker, but I've seen French presses and I thought the idea was that they aren't very expensive, but they're a lot more laborious than a machine, both in preparation and in cleaning.
It's kinda like my fancy tea infuser cup: I have a nice glass mug with a laser-cut stainless-steel infuser for loose tea. It was $30 at a fancy store (could probably get it cheaper on Amazon), but it's a one-time purchase. With high-end loose tea, it makes great tea, but the problem is cleaning: cleaning out the infuser (by hand) is a lot more work than just dumping a tea bag in the trash and putting a regular mug in the dishwasher. But the results certainly are a lot better than a $0.20 tea bag.
They're not that bad. I rinse them out after use and then put them in the dishwasher. Preparation is like making a cup of tea, just pouring some hot water in. I would say prep takes <2min for a pot of coffee (including filling up the kettle), cleaning <1 min.
The problem with the infuser is that there's only one of them, unlike regular mugs where I have a whole bunch of them because they're practically free (they're a common gift item, after all). The infuser set-up is expensive, so I'm not going to buy 5 of them so I make tea frequently with no cleaning, so I need to hand-wash it. Regular mugs aren't like this: I can just use them and toss them in the dishwasher and get another one when I want another hot drink. And you're right, it's not a huge amount of time to hand-wash, maybe about a minute or so, but it's still a lot more than the utterly trivial amount of time it takes to put a mug in a dishwasher.
Stove top espresso and simple milk frother that I own 1) makes better coffee than I've ever had in Starbuck because I buy good beans and 2) costs $30. Admittedly I spent $200 on a grinder so I could fresh grind finely as it makes a significant difference to the coffee IMO however I could just as easily get my beans ground when I buy them for free.