I see no reason to do so and wish this wasn't even happening. We have many samples of Forrest's DNA around after all, locks of hair in various places I think, and items like this vest in a recent thread with his DNA all over it:
https://civilwartalk.com/threads/general-nathan-bedford-forrest-vest-sells-for-amazing-price.184979/
As for proving whether or not many of the claimants of his bloodline, I imagine many of them wouldn't want to risk their claims proven true or false, as it would be scandalous right now if the latter and they probably wouldn't believe it anyway. Lots of numbskulls, some who've written laughable books about Forrest are most likely not related at all and have have everything to lose.
Speaking of which, I wouldn't be surprised if many of the "Forrest Family" that the SCV is using to profit from the remains have no relation to the good General and his wife whatsoever.
But for all I or anyone else knows, Tennessee law may require such a test to confirm they are who they most definitely are when exhumed. It would be hilarious if the imbeciles who gave the remains to the SCV are exposed to be frauds, and could be a good thing in my book. He'll just get dug up again in ten to twenty years going where he's going after the banks foreclose on SCV HQ and it dissolves due to bad policies and lack of new non-gray haired recruits, and then they may not get a final resting place then as the history destroyers get more radical by the day.