Well, reason for inactivity is that it works as intended.
As for if it is needed or not, that depends on your setup and your needs.
As for the 'is_logged_in' cookie, no. 4.4 only creates a session cookie when it is needed so you should instead avoid caching the request if there are cookies (esp session cookies) in the request. In other words closer to how all proxies / reverse proxies works out of the box.