I never use my profile to investigate my recent rep changes. I use the dropdown that appears when I hover over my name. I also never click the "see your profile" links in the notification part of the super collider about new badges, though I may click the link on the question.
I use my own profile for "I think I asked/answered/commented on that recently" to get a link that I can then use in a comment or answer, or to close something as a dupe. I also use it to check up on a flag that I might remember casting (typically not on SO but on lower volume sites.)
I like the big graph-of-everything, so I often use my own profile on any random site as a way to get to my network profile and look at the graph.
I use other people's profiles most often from meta when they post a vague question complaining about what happened to one of their questions but without any links - meta profile, SO or whatever profile, look through questions and figure out what happened. I rarely use them for any other purpose. I try to interact with questions and answers as content and not too much as products of actual people. The exception is people who have built up a virtual profile in my head from their questions and answers - I rarely supplement that profile with looking at their online one. Occasionally I will check for a twitter handle or other contact method - but that's perhaps once a year.
I don't think of the current profile as broken and wouldn't want to see it change much. I think people vary so widely in what they want that the best approach is to provide lots of it and let us choose. The one exception would be the paging behaviour on the lists of questions and answers. If you page through to page 7, click a link because you think you've found what you want, then click back - you're on page 1 again. I dislike that.