OK, the problem is NOT the supply of dead people. Clearly, the annual production of dead people vastly outnumbers the people who need organ transplants.
The problem is that you can’t simply use organs from any old dead guy. Grandpa slips in the bathroom, dies of a head injury, and is found a week later? Sorry - no usable organs. Person dies of cancer? Sorry, can’t use their organs - you’d likely be transplanting cancer cells along with it, into a person with a suppressed immune system. That would not end well. People with hepatitis, HIV, rabies, and bunch of other diseases? You’d be transmitting the disease as well (and yes, the US had a donor with rabies slip through the net, resulting in the deaths of all recipients of his organs). 100 year old dude? Probably not a suitable donor. And so on.
In order to get a viable donor organ (outside of live donations) you need a donor who is dead, but not too dead. Brain dead, specifically, but maintained without interruption on life support so their organs are kept alive and in good condition. The problem here?
Very few people die in that manner.
Mostly, it’s young people dead of brain injuries caused by an accident - and they would have to be still breathing up until at least the time the emergency personnel got to them, and kept oxygenated until it’s finally determined that they aren’t going to get better, their brain really is toast. If, for example, someone dies of a head injury in an accident and stops breathing long enough it doesn’t matter if you get their heart going again - it’s not just the brain that is affected by oxygen deprivation, just that the brain is affected first and worst. If someone has a traumatic injury and dies in the ICU later they may not be suitable due to organ damage sustained as their condition deteriorates, or due to infection, or whatever killed them other than the horrible accident they suffered. You might think burn patients who later expire in the hospital might be good donors, but the body’s reactions to large burns can cause all sorts of organ damage so no, they’re not good donors, either. You really need someone who dies of a brain injuries, and fairly quickly after the damage is induced, but not too quickly.
So the problem isn’t the number of dead, it’s the number of dead who die in a manner that allows for organ harvest. There aren’t enough of them. On top of that, if you’re a donor with weird immune characteristics you may still be screwed because not just any ol’ body part will do, you need a match and if you’re an outlier you might just not have a match die in the “proper” manner before you check out.
The percentage of people who die in a “proper” manner so as to leave them potential organ donors minus all of those unsuitable for other reasons isn’t a very big number.
So, while mandatory donation would increase available organs there still won’t be enough to go around to all who need them.