It's systematic.
Successful white high school players (RBs, WRs, DBs) don't get recruited by big university programs.
So they either
1/get moved to another position;
2/have to walk-on and work their way up the depth chart; or
3/ go to a smaller school (very common )
If they are successful at the college level, it's often at a smaller school, and so they don't get much attention or get drafted.
So then for the NFL, they have to:
1/ move to another position - FB or special teams;
2/ walk-on to an NFL team and work their way up the depth chart;
3/ go to another league
Frankly, I think all these guys should go to the CFL and tear it up there, then being put through the B.S. in the NFL.
NE is the only team that really sees value in white skill players, but they are very smart about it monetarily. They know that no one else is going after these players, so they can pick them up for no money. It's supply and demand. There are no other teams demanding these players, so they don't even need to draft them. In the rare case that someone starts to make big money, i.e., Welker; they can let him go and pick-up someone like Edelman for half the price.
They are very savvy in recognizing that they can get white skill players cheap, because no one else wants them..... by the way, where is Welker now?