> It's opt-in now, and easy to opt in, yet despite many people saying they support it, few opt in.

Let's take this as a fact. You don't solve the problem by flipping this around, because then you only solve for social gain. You just make it worse for the individual:

> It's opt-out now, and easy to opt out, yet despite many people saying they don't support it, few opt out.

Now you have people not supporting (or wanting to remain blissfully unaware of) donorship, registered as donors. You bank on apathy and ignorance, because a simple and deliberate opt-in was not convincing enough, and turned supporters for or against, but still, for whatever reason, on the fence, into fair gain.

Having your cake and eating it: If it is very easy to go through opt-in process, yet there are problems with registering a deliberate choice, then it will also be very easy to go through opt-out process, but there will be the same problems with registering a deliberate choice. The ease cancels out, and the problems remain. But taking away a human right, until registered protest, is far worse than a deliberate opting out of it.