I disagree with you though that vaccines are any more important than agriculture in reducing future mortality..
I think it is important to note that I did not say they were more important - I was saying that they are more a
current and
immediate concern. At the moment they have several diseases "on the run" so to speak - with several more years of effort they have every chance of eradicating the diseases. Whereas, if we stop or reduce efforts, the diseases will have a chance for a comeback, and all previous work will be largely wasted (I say largely because of course the individuals that were vaccinated benefit from the vaccination - but the goal is not vaccination so much as eradication).
It's not a foregone conclusion that these diseases will be eradicated - the Gates foundation is fighting against local religious prejudices, for one thing. But it is reasonably possible, and would be a great result if achieved.
Let me try for an agricultural analogy. I'm sure it'll be off in some aspects because I am not in the field - grant me that. Suppose there was a blight that, with a few years work, could be eradicated. The blight has the possibility for some localized starvation if the towns do not have a lot of various crops, etc. And, we have the science to completely eradicated the blight, but it will take some money. Doesn't it make sense to attack this problem, now, while it is tamped down and amenable to eradication, even though we of course have longer term issues with sustainability, production yields, etc? Ignoring the blight will just let it get worse, and waste all of the effort made on it to date.
IOW, it makes sense to put money, sometimes a lot of money, towards a smaller problem if we can completely eliminate that problem. It's not a judgment that the longer term stuff is unimportant, or less important.
And things like polio are anything but 'small'. It used to be a devastating disease, and a global problem, with epidemics sweeping across countries. I assure you that you would not want yourself or anyone you know to have it. We have fought against it to the point that it exists only in small pockets. With a modest investment we can eradicate it. It's an extremely important goal - if we don't achieve it the disease will have the opportunity to grow, perhaps even mutate. We really need it gone, completely.
There are very few major problems in the world where a few billion dollars might be enough to change things
for the rest of history. As you point out, the agriculture issues are many, and require a multitude of different approaches to really solve starvation. It's not just yields, it's not just technology, it's not just politics - it's all of that and more.
The Gates Foundation spent a lot of time thinking at the beginning, trying how best to invest money. There is no obvious answer. But they have taken the approach of 'best bang for the buck' - you could poor billions into, say, the Israeli/Palestine problem and not make a dent in it - it would be as if the money just evaporated. The Gates Foundation chooses to invest where they can make large differences in people's lives - getting rid of diseases, improving water sources for farms, that sort of thing, with the idea that if you reduce misery and get rid of things that keep people at the most impoverished levels, they will have the chance to live a meaningful life and start participating in improving their lot. If you are starving, or dying in a hospital, you can't help yourself. If many of your kids die, you will be procreating like mad, causing population explosions. You have to nip that stuff in the bud. On the back of that you can then usefully make the needed improvements to agriculture, infrastructure, etc. If you and your kids have polio, et. al., you ain't going to be able to put better farming practices into use - you'll just be laying on your bed, dying or sick.