All these three problems, as well as most future problems come from corrupt distribution of resources.
Once humanity invented agriculture, we set ourselves on a path no different than other creatures who are not nomadic. Think ants in a steep mountain valley, or a pride of lions stranded on an island. All resources are eventually consumed and the society collapses.
We have the ability to plan further than the ants so we can compensate for temporary changes in resource abundance. We can divert water more than ever, but each new diversion has more of the 1% in mind rather than the 99%. Think data centers in the desert making the BTC holders richer at the cost of next years crops. Look at all the planned communities going dry world wide because developers did not worry about future water. Build a few divisions, go bankrupt but the owners still make money. Repeat as needed.
Nuclear war will not happen because of unequal rights, poverty or honor - the ones in power do not care about such things. Riots will not lead to nuclear exchanges. It's going to start somewhere in Asia/Indus over water.
Corrupt distribution of resources only can solve up to half of the equation: the economics of society. It does not solve most social problems including drug addition, depression, and personal bullying. For example, EU government officials can often have the following things which you can't: nuclear bombs, crack cocaine, and EU banned books (such as stored in an evidence locker). Crack cocaine is part of the drug war, a major source of social problems. If society had good overall virtue and equal rights, it would either voluntarily avoid crack cocaine, or allow crack cocaine and handle it as a medical and psychological problem rather than a legal problem. Maybe, in places where a high enough number supermajority of people think crack cocaine should be banned entirely, the ban would actually work for the most part even if having minor problems could result and potentially be slightly larger than the one being solved, but wouldn't be noticeable because such a small number of people were effected by the ban. Stealing or damaging other people's property is wrong, and a politicians drug war involves doing both of those. Having virtuous and proper distribution of resources does not address crack cocaine addiction or the corresponding property right.
I do think corrupt distribution of resources leads to unequal rights, but also the acceptance of unequal rights leads to corrupt distribution of resources. Even though corrupt distribution of resources did seem to come first, it is the acceptance of that concept that causes it to persist. With equal rights for all, it would be quite difficult in today's world to corrupt the distribution of resources.
Overall I'm in agreement that it would be quite a good point that corrupt distribution of resources would encompass the bulk of societies problems, and one could state that as a block of societies biggest problems, but I do think it could be secondary to others depending on definitions of terms. I look at society as not being naturally good for that reason of wanting the inequality. I believe civility is a learned behavior and something that can be adopted from the spiritual and philosophical people of society. Whether that can only be done by non-violent means is something I have not thought of. The USA and others did acquire a lot of rights and freedoms after physically attacking colonial powers who were unfairly distributing resources, and those rights and freedoms have been adopted by many other countries, but whether that could have been accomplished another way I don't know. I do realize there are extreme challenges in assigning land ownership rights for example and that is well on track to becoming a major issue of contention as the land becomes further consolidated by the wealthy.
Thanks for bringing up this point, I appreciate that greatly and will be mulling this over for a while!