Some of us have questioned why Harry had to continue to spend several weeks with the Dursleys each summer after Voldemort returned at the end of GoF. If sharing Harry's blood allowed Voldemort to touch Harry, then it seems logical that it would also allow him to bypass any magical blood protections on #4 Privet Drive. So here's an idea, inspired by Arsinoe de Blassenville's
The Best Revenge.
Dumbledore could argue that the Dursleys should have custody of Harry, even though they were Muggles, because Petunia was Harry's closest living blood relative. However, his argument probably would not have been especially valid unless Harry had actually lived with the Dursleys for at least a few weeks each summer. If Harry never actually spent any time with the Dursleys, then more distant wizarding relatives might have been able to present a good case for why they should have custody of him instead.
For example, let's suppose that Harry was the grandson of Dorea Black and Charlus Potter on the
Black Family Tapestry. In that case, it's quite possible that, in the summer of 1995, Harry's closest living wizarding relatives (who were not convicted criminals anyway) were his second cousins Andromeda Tonks and Narcissa Malfoy. In the summer of 1995, Andromeda Tonks had long since been disinherited from the Black family, and Lucius Malfoy had the ear of the Minister of Magic. So, if Harry hadn't continued to live with the Dursleys for part of each summer, then the Malfoys might have been able to gain custody of the Boy-Who-Lived.
In a sense, then, the Dursleys did provide Harry with a "blood" protection, even after Voldemort returned. But it wasn't necessarily a magical protection; it was a legal one.