Yes, you're right about that. But we should also provide the correct
cropping functionality so the user does not end up doing it himself in
paint to get the correct resolution. And the user does not notice the
background processing that is done. Only the result is more like what he
expects.

I am also not happy with this option in the settings, because it is
nothing that needs to be configured every week and would need some
explaining text what it does. Perhaps the personal page fits more.

Personally I would be fine with a maximum width of ~600px because that
fits my phone, but every user's phone may have a different maximum
resolution (what about tablets?). I also don't care if the traffic is 10
times bigger. But what about other people in other countries that would
be happy  to decrease the size to 100px to save some bytes on their
mobile plans?
These are the reasons why I would make it configurable.