People on Sufficient Velocity (and the wider scifi/fandom forum ecosystem) seem to have beta readers, at least many of them open their fics/chapters with credits to 1-3 beta readers, and most of those people are def the "youth" (mostly university aged mix of aspiring writers and misc fannish people).
I think that getting beta readers requires a space which promotes organic conversation about your fic and fic like it in the same space as the fic itself (i.e. forums), so you can form relationships founded on the idea of the fic being cool and interesting and worth talking about and then you can ask those people to beta-read for you and this is an enthusiasm-provoking shiny thing rather than a chore only performed for the sake of reciprocity? I don't know how much they get out of it, but they seem enthusiastic about it, their credits are usually pretty glowing.
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I think that getting beta readers requires a space which promotes organic conversation about your fic and fic like it in the same space as the fic itself (i.e. forums), so you can form relationships founded on the idea of the fic being cool and interesting and worth talking about and then you can ask those people to beta-read for you and this is an enthusiasm-provoking shiny thing rather than a chore only performed for the sake of reciprocity? I don't know how much they get out of it, but they seem enthusiastic about it, their credits are usually pretty glowing.