Like an eternal contract? "If the state gives you benefits, we have all rights to your body". Seems pretty morbid to me...
And who would say it stops at organ donations. Going on the argument of "they're dead, do they really care if their body has the original organs or not?", couldn't you go the whole 9 yards and say "they're dead, do they really care if we inject their body with hormones and see what happens?". Because i'm pretty sure your loved ones wouldn't be too happy with your body being hacked and cut away, whether it's for science or to save lives. Because once you sign away your body saying that your organs are up for grabs, who's to say what they'd be used for
Your family still gets a box to bury, or burn, depending on their preference.
It's not like people will be asking "where's the body-parts?" at the funeral.
You're not going to be saying, "sorry, the government took the body to run tests"
Donors are buries/cremated all the time. I for one don't really want to know what's missing, although a letter of thanks from the person saved would probably go a long way towards making the greiving family feel better.
When I carried my old-mans coffin, it felt like there was nothing in it, and we joked that anything that wasn't already pickled had probably been stripped out of him for spare parts. It really doesn't enter your head that it's a bad thing. The grieving process is still the same.