No it wouldn't be cool. It would be a HUGE security because this is a multiuser blogging platform ie. our blogs are not free standing they are all on the same multiuser blogging platform.
This is just a basic part of the underlying technology of the web browser, and it’s required for sites like gmail, Yahoo!, and others to operate.
There are ways a site can avoid this problem (generally by constantly changing the login cookie data with EVERY response, and invalidating the old ones immediately), but they require more horsepower on the backend than the blogging sites are really able to provide, and there’s still usually a small window of opportunity.