I was actually basing this argument off of a similar one which gives much shorter windows (like ~1 Myr or something) as an upper bound on the amount of time a civilization can exit, which makes communication with other civilizations even more unlikely. This shorter bound comes from the very pessimistic notion that advanced civilizations will inevitably destroy themselves (e.g. nuclear holocaust). Obviously this one is a somewhat unfounded limit, but one could interpret the Fermi paradox as an empirical basis for the macabre hypothesis >:)