On one hand, I don't want to be tracked. Disabling cookies in this case is fine, because if I open my webmail then all I do afterwards is tracked, courtesy of analytics code. On the other hand, disallowing cookies leads to all the problems mentioned in the post.
I wish there was a feature "keep multiple tabs, but cookies are not shared between them". Currently I manage with a combination of Firefox extensions and using two browsers at the time. But I wish it was easier.