Mustang Sally posted before me and had some really great points. VKM is multi-generational, so it only makes sense that he is big on that. also, the whole family oriented wrestling entertainment making mention of wrestling families is also a very easy link to the audience.
PhD also had the very good point that it just makes more money with merchandise and tv and buyrates, etc. money is a pretty powerful influencer.
but to the original post, i do remember very clearly that The Rock was billed as a 3rd generation wrestler from the very beginning. like, from his debut match at the Survivor Series... "the grandson of the great High Chief Peter Maivia and the son of the great Rocky Johnson" it was acknowledged from the very beginning.
now with Rikishi and Yokozuna and Rock and Rosie and Haku, there never was any mention of the generations (except for Rock of course) but i think it's because that with the exception of Rock, they were all the patriarchs of the family. the thing that got me more was that they didn't form a huge and powerful "Samoan Family Stable", but that's another story. this would be one of the few times that WWE did not "cash in" on somebody's family history. that's my point there.
but i even remember Mr. Perfect being billed as the son of Larry "the Axe" Hennig from the very beginning and that he was a great 2nd generation wrestler. same goes for Bret and Owen Hart and being trained under the legendary (and old! thanks Jerry Lawler for all the great jokes!) Stu Hart in the infamous Hart Dungeon. even guys like Lance Storm, Chris Benoit and Chris Jericho got the rub, so to speak, just for having trained there.
i also remember the Million Dollar Man Ted Dibiase being known as the son of "Iron" Mike Dibiase.
there was always a teased relationship about Grand Masta Sexay being the son of Jerry Lawler.
Guerrero and Mysterio have been very well connected with their family history and legacy, at least in the WWE, and there is constant reference to their growing up in wrestling families and being multi-generational. Chavo Jr especially got this nod.
Goldust was known as "the American Nightmare", a not-too-subtle reference to his dad, "the American Dream" Dusty Rhodes. and throughout his many gimmicks and turns, he's referenced himself as Dustin Rhodes (or Runnels, whatever) more than once. and not just Goldust, but the announcers as well.
i guess my point in all these mentions is simply that this is not new. not at all.
and of course, now, you have guys like Randy Orton, DH Smith, Dibiase, Cody Rhodes, the Uso's, etc. so now they're everywhere, but i've got the memories of this being a big deal and at least more than a casual reference in the past too. i dunno that it's so much a "new" thing now as much as it is just the "biggest" thing now, as far as Vince's push and security in having them around.
again, to quote another poster, with multi-generationers, you're much less likely to have them jump ship at the height of their popularity and push.