Yep, you certainly can, which is part of their the beauty.
Last I looked, though, you couldn't deploy to S3 without using tools that work specifically with it.
I guess it's really not that big a deal, but I prefer the genericness of "I'm configuring a webserver and pushing my files to it."
That process can be just about fully automated, even including HTTPS setup if you want that, and then you can use with whatever server provider you like.
Depends on the tools! If you're manually copying files, there are clients (e.g. Transmit, which is what I use) that just treat it like any (S)FTP server. If you're using the command line, yeah, you need to use Amazon's CLI, although it's still basically a one-liner to sync the directory you want to publish.
Last I looked, though, you couldn't deploy to S3 without using tools that work specifically with it.
I guess it's really not that big a deal, but I prefer the genericness of "I'm configuring a webserver and pushing my files to it."
That process can be just about fully automated, even including HTTPS setup if you want that, and then you can use with whatever server provider you like.