Which is why most reputable hotels will ask for a photo ID when running a new key. At least that's the procedure I had to go through when I last forgot my keys in my hotel room and locked myself out.

The simplest method to get into a room is to wait for it to be cleaned, and once the door is open, simply walk in and take whatever you want. The maids will not ask you for ID. If you want to make it seem extra plausible, wave a similar hotel key at them as if you would have used it to open the door.

As for getting a replacement key, yeah, that usually does require some work. In lieu of asking for a replacement you can call the front desk on your cellphone and tell them you're standing outside your room and can't get to your key, and can someone come unlock the door for you.

Wouldn't it look odd to be loitering in a hotel hallway?

That never happened to me, even in hotels with guards wearing pumpguns and elevators that needed key-cards to be inserted if you wanted to go up (e.g. the Marriott in Paramaribo).

And it's all on video camera (pretty much all hotel lobbies have them), whoever made a copy of a key remember it, etc. Many hotel corridors have cameras too. It's not as easy as you think to get copy of the key and enter the room without leaving evidences.

Who says they did it without leaving evidence? I'm sure there's security camera footage somewhere (presumably deleted by now, but maybe not). It's not like they're going to put out an INTERPOL warrant based on some grainy security camera footage of just-another-dude-with-a-beard walking into a hotel room.