It all comes down to consent.
I can consent to all or some of my organs being donated at any time but after my death the surgeons need consent to do the surgery to harvest said organs from my body.
I am legally dead (though my body will be being kept going artificially to give the organs the best chance if a transplant is consented to) so I can't consent to that and they have to ask my NoK.
The problem arises if your NoK has different wishes to you or does not know what your wishes are, because their decision overrides any wishes you may have held previously as it's their signature that is needed on the consent paperwork.
Equally your NoK may have more recent knowledge of your wishes changing and so they have the right to override your wishes - eg if you'd always said "take anything" and have always been registered as such but then in the last few years you'd become squeamish at the idea of someone taking your corneas and told your NoK this, when it comes time to consent to donate they can say "Actually you can take anything *except" the corneas as I know she changed her mind about them recently"
If you're registered then you can set out your wishes to make them explicitly clear but that is essentially the guideline the medical team can give your NoK when they make the decision (IE "She has it recorded that she wanted to donate XYZ, do you have any objection?") as opposed to it being legally binding.
Some dislike it but I think that it is the best system as it allows for you to set out your wishes but the NoK makes the ultimate decision as they may have more recent information ... For example if the OP had posted this thread saying she was about to take herself off the register but then got run over by a bus on the way home before she did so then if the law was "we go with registration only" then doctors could take whatever the wanted, even if the OPs NoK knew she intended to remove herself from the register, as they would have no say in the matter.