Yes, because they don’t want the burden of storing that data, which they would have to in order to attempt to verify you, they know they aren’t network security experts so do they really want to open themselves to the potential risk of storing copies of ID’s?
Phone number verification is, for the most part, worthless, you can get temp numbers online for texts and you can get free pay as you go sim cards, so that doesn’t solve the issue for people who actually want to exploit the system properly
Age verification is just as annoying to deal with so mostly isn’t bothered with unless the site specifically caters to NSFW content, which in this case MW does not
They don’t have to worry about that, they comply with any removal requests and that is all they are legally obligated to do, look up the “safe harbour” clause in the DMCA, it protects service providers from being sued for content their users upload aslong as they meet certain conditions, things like timely takedowns when requested etc