Why did Obi-Wan allow Leia to get adopted by such a high profile figure?

I know that Leia is a princess because she was adopted by the Queen of Alderaan, but why would Obi-Wan allow this? Wasn't the original plan of Obi-Wan and Yoda to hide the Skywalkers from Palpatine? Luke was placed into a very low-profile position, being the child of two farmers on a backwater planet. However, Leia occupies a very important political position.

Is there any reason why Obi-Wan would do this if he was trying to hide her?