The problem is that White is completely unproven. And I feel you are overrating the other guys when you consider how much actual starting experience they have. The only guy out of that group I have moderate trust in is Blount. Reggie Bush on reasonable money? I like that move because he's a proven 3rd down back, and we don't need him long-term, we just need him to be good 1-2 seasons until we train up a replacement.
Don't forget that when we let Woodhead go, Vereen had shown signs that he could be the 3rd down guy by destroying the Texans nearly single-handedly in the playoffs. OTH White has done NOTHING to make me think he could be ready yet.
Maybe White is "completely unproven" to us, as fans. But the coaching staff has seen him for an off-season and a full year. If they're not convinced, then I grant we're likely to sign Bush or Spiller to fill the spot. But we shouldn't take the fact that White was buried behind Vereen as evidence that he's a bust.
IMO, fans are too inclined to believe that a prospect is unable to contribute when they're buried on the depth chart. The version of Edelman we saw in 2012 and 2013 didn't seem like a very promising solution at WR. The uproar on this site when anyone suggested that Edelman step into Welker's role was historic, and not unlike what we're seeing this offseason with Revis and Vereen leaving. When given his chance, Edelman stepped up big time and changed people's opinions.
Hightower is another guy that a lot of fans on this site gave up on too soon. It wasn't until Spikes was gone and Mayo was injured that the consensus started to shift in his favor. And now he looks like a long term cornerstone for the D.
If Vereen had torn an ACL, we would have seen a lot more of White this year, and actually had a basis for evaluation. The fact that Vereen was healthy and productive just means that we have no idea about White, which is different from knowing that White's upside is limited.
The fact that BB didn't try harder to keep Vereen around is a clue, for me. If he didn't think he had options on his depth chart, or in free agency, or in the draft, Vereen would have been worth a little more effort.
Final point: no reason to assume that Bush or Spiller or any other vet would transition well into the Pats scheme. There have been expensive veterans that were successful elsewhere that washed out in Foxboro. Maybe trusting in White is a risk-- fair enough. Well, trusting in Bush is a risk too, and a more expensive risk at that.