I agree with the idea that login should take person to their own page. But, there still should be a page to see the “stats” (default or custon), on this day, etc which currently is My Page. Maybe the name is misleading but not sure of alternate. Even I look at it and use it for my own HTML block of details.
That is absolutely my own thoughts, and I’m also struggling to find the right name for the page.
But another option is to allow small blocks (renamed as “widgets” ) to be placed on one side of ALL pages. A bit like this site.