This leads to the (new) product registration page but not to an account overview page.
I think it should be possible to "just log in" to an account and see what's going on there - like it is possible to log into a bank account and see what's going on there. What if I just want to change something like address, or email, or want to unregister a product because I sold it?
In my opinion it is strange that Apple is not offering such a login link, at least not clearly visible on their website.