You typically do a 302 redirect AFTER the POST authentication. This feels more of a publicity stunt more than anything. It might affect very few use-cases. Bulk of the requests on the web are GETs anyway.
I agree. Facebook redirects a successful login POST with a 302, which then results in a GET to '/'. This is an extremely common pattern. Once you're making GETs, 'fresh' resources can be served from cache without revalidation [1]. This is basically the whole point of the fresh vs. stale distinction.