The idea that you can only be family by blood

I was thinking of the first movie today - how Dumbledore leaves Harry at the Dursleys' doorstep, even if McGonagall is against it. We are told it's because they're the only family he has.

It's so weird to me that whatever protection was offered by Lily was blood-bound. If it was the power of love that protected Harry, couldn't love be the force that could continue to protect him? Surely there would be many families who would be happy to take him in - people that Dumbledore personally knew and could trust. I get that Rowling wanted him to have a Cinderella story, but even as a child who adored HP, I couldn't understand why this was so.

Not to mention the Dursleys never wanted to take Harry in and didn't love him.

Of course, we know by now that JKR's world building is rather weak, so this isn't too surprising.