I do think it's important that the more generic and obsolete a question is, the more effort we take to make note of that fact.
Having said that, it's not unheard of for some players to deliberately avoid updating to the latest version for some games—Dwarf Fortress comes to mind, wherein some people chose to continue playing the 2D version after Z-levels were introduced. Minecraft represents a similar issue, as I've seen some comments on places like Reddit claiming intent to maintain pre-1.8 worlds and content by preserving an older version of the game. Similarly, games that are updated to provide more metagame restrictions or to remove popular bugs can also lead to a schism in preferred versions: when manufactured copies of Metroid Prime started appearing with a couple popular speed-running tricks disabled, a handful of new players decided they'd only buy the game if they could verify it was an original printing.
So while I agree that out-of-date questions should probably be addressed whenever the game is updated in a relevant fashion, I don't find the gamename-beta tag particularly useful, as pre-beta and post-beta is not the only case where questions become out-of-date. I myself have had an updated answer to an out-of-date questionupdated answer to an out-of-date question surpass the original answer in votes, and it is frustrating to have to wonder whether the original asker will ever even see it; duplicating the question and documenting the out-of-dateness of the previous question does strike me as the best solution.