Since Mel Blanc passed away, doesn't his son do the voice of Bugs Bunny and his other characters?  And if not, why not?

Mel was amazing.  To "replace" him, it's required a whole squadron of voice actors including Greg Burson, Jeff Bergman, Billy West, Joe Alaskey, Bob Bergen, Maurice LaMarche, Mindy Segal, Neil Ross, Frank Welker, Frank Gorshin, Bill Farmer and at least ten others.  Some of these gents are the frequent voices of certain characters — Porky Pig is usually done by Bergen, Daffy by Alaskey, etc. — but no one seems to have an absolute exclusive on any role.  This is partly because various folks at Warner Brothers disagree on which actor does the best Bugs, who sounds most like Foghorn, and so on.  It is also because, by always having a large talent pool from which to pick, it prevents any one voice actor from demanding massive sums of cash…as Mel often did in his last decade or two.

In interviews he gave late in life, Mel sometimes said that his son Noel would take over his roles some day…and Noel reportedly did some small parts even while Mel was still with us.  Noel Blanc has also done a few roles here and there in the years since, usually as Tweety or Porky.  However, he is quite successful in other lines of work and apparently uninterested in spending his days locked in a recording studio.  So, by mutual agreement, others usually do Bugs and Friends.