Belliard has no range for throws at 1B and should never play there. He's way too short. But Nick has never been very good at picking balls in the dirt, and that is continuing. Throwing errors are saved by picking first basemen. I don't expect Dunn to make those plays either (although he may get there with extended work), but those throws in the dirt cost us with Nick anyway. We may prevent a high throw or two with Dunn, but we also pick up fielding errors.
Dunn at 1B without a rangey 2Bman is a prescription for a lot of ground ball singles to RF.
I wholeheartedly disagree with your assessment of Nick. I watched him play a good deal of 1B when he was with the Yankees and he was really good a going down and digging out errant throws. Yesterday he successfully saved at least two (and in my opinion three) separate errors - one by Zimmerman and one by Guzman, both on errant throws in the dirt in front of him.
NO WAY Dunn gets to that level ever. He can hardly chase a ball around the outfield without making it an adventure.
Nick is a much better defensive 1B than you give him credit for.