For sure this has changed tremendously since we all were kids. If you’re not a frequent hotel user now, your gut and experience from 1995 or even 2015 isn’t real relevant to current practice.
Key cards:
Key cards are both reusable and disposable. They’ll never know or care if you take yours. But all else equal, it’s nice to leave it behind, whether in the room, on the front desk, or in a drop box, secure or otherwise.
The key only contains a code number and a drop dead time. If someone came by behind you and grabbed your key from the front desk counter, there’s nothing useful they could do with it unless a) they knew which room you came from, and b) they did their dirty work before checkout time. Anyone who has access to the computer to decode which room that key went to also has the access to make a fresh key for themselves.
So worrying about the physical security of the key after you’re done with it is just silly.
As to checkout w the staff:
I’ll stop by the desk on the way out and drop my keys. In the box or on their recessed desk, not on the countertop. I’ll talk to the clerk if there’s no line. My usual habit is to eat breakfast immediately before leaving and I’d like to ensure that charge did get onto my bill. But I sure won’t wait in line to do that. And nowadays I feel silly even doing that much.
Like every business everywhere, they are using whatever tech they can to reduce touch labor. And that includes front desk people. Which means, as somebody said upthread, the only people talking to the front desk are either people with complicated issues, or people who don’t know how to play this game. Or at least not how to play the current version of this game. As a result, the typical front desk clerk interaction takes several minutes. And they have very few clerks. So any wait in that line will be interminable. And probably a stupid decision on your part.
As to housekeeping:
If I happen to pass the maid in the hallway I’ll interrupt them long enough to say “I’m out of room 321”. That seems polite, minimizing the likelihood that poor frazzled underpaid person is left waiting until time X then saddled with too many rooms and too little time. It’s a courtesy to the worker, not to the giant corporation.
Story time:
When I was working, things were a bit different. The company reserved and paid for the rooms, but we were responsible for any incidentals. Walking out on a room charge led to hassle for the company and contributed to desk clerk hostility to all your identically-dressed interchangeable cog-like coworkers who’d be staying there every night for years. Meanwhile, if you used your hotel affiliated credit card for incidentals, and attached your hotel frequent-stayer number to your stay, you got some spifs for that.
So putting your card and loyalty number against your room at check-in was routine. As was ensuring your incidental bill was correct and settled on the way back out. I’m still breaking that second habit now that I’m retired. They’ll get my charges straight enough for my purposes. And theirs.
ETA: Ref @puzzlegal just below. All the above applies to modern corporate hotels pretty much world wide. But does not apply, as she said, to Mom’n’Pops, one-off boutique places, B&Bs, etc.