I may be strange, but I probably would watch a fully episodic post-apocalyptic TV show. The Fallout universe would work really well for that, in fact. Do each game as a separate season, but instead of following the Lone Wanderer follow an ensemble cast. Fallout 1 would be based out of Shady Sands, Junktown, or the Boneyard, and each week either something threatens their settlement or they venture out into the Mojave and discover something. Do an old-fashioned 20+ episode season to let the show breathe and escalate to a finale with the Master in the final few episodes.

An episodic format would allow you to rotate through genres. An episode dealing with the raiders plaguing Shady Sands would play like a Western or maybe Mad Max. A later episode could be horror focused and simply titled "Deathclaw".

Nobody but me would want this though, and certainly not the modern screenwriters who always have to fit everything into a 10-12 episode series.