The piece of the TARDIS was one of the clues pointing to a big-ass reset button in the Doctor's future. I'm sure the annals of history could survive the loss of Rory, but the TARDIS wiped from history?
Counter sets back to zero, we get a new TARDIS (please no changing the outside-- though I can see that happening) and a new Doctor #1, perhaps?
Possibly - it would get rid of that pesky regeneration limit but then I suspect we'd just ignore that anyway
A brand new TARDIS would have to explain why it still can only look like a phone box, of course.