I agree. If you want your placenta, you should have it. I can't think of an excuse not to let someone have it, other than a Gulliver's travels yolks-up-yolks-down culture clash.
Frankly, I thought it was kind of cute-looking, not gross looking at all, oddly firm and floppy at the same time, and such an interesting shape, and I sort of had an urge to keep it (from my son and his mother) around for awhile, as a souvenir. I'm pretty sure would have changed my mind after a few days.
I'm not hungry for placenta at the moment, but I don't see the big deal about eating a placenta. Waste-not want-not. It is common for carnivorous animals to eat it. I think even some herbivorous animals eat it -- helps prevent predators from tracking them.
A removed organ or limb I'd probably feel uncomfortable keeping around. Constantly reminded that it is in the wrong place (on the bookshelf, instead of attached to me), but a placenta is supposed to detach itself from mom and baby. So it wouldn't be so unpleasant to have around. Seeing it would remind me that things went happily (assuming the mommy and baby are well); seeing an organ around would remind me that I lost an organ.