Yes, it's a property rights issue.. and more. The problem is motivating those who are holding on to the food to distribute it to those who need it.
Clearly if those who need it are providing valuable service to food producers and distributors, there wouldn't be a problem.
The issue is really, how do we motivate the distribution of food (and other goods and services) to those who need it but can't justify to the producers and distributors and provide for it?
One solution is definitely charity. You pay the producers and distributors to distribute it to the needy. However, this quickly becomes a system that is easy to game. Often it's easier to convince the donor that work has been done instead of actually doing the work.
Another solution is government welfare, but it really comes down to the same problem - the objective becomes just convincing those asking for it.
The central issue is that those who need it but can't justify it are essentially powerless to motivate others to provide for them. IMHO the only reasonable way is to help these people become net producers in the economy or have more political power.
People shouldn't have to justify their existence based on some other group's favorite economic model. That seems weird and needlessly cruel.
How is it "the thing", unless "the thing" is supposed to be, what, people using common sense? And how is it "the thing that causes these problems" when those problems are the natural state of being? People don't have food by default, people don't have housing by default, the huge amount of food being produced these days is in no way the state of nature. The argument of EA is closer to: doing more of the things that currently feed 95% of the world is the way to feed 100%.
How do you know it's not doing more of the things that currently leave 5% without food?
That is purely a political choice. Just grow the food supply faster than the population. Most developed countries have solved this on the population side. If every EU country had 0.5 - 1 billion people all of them would run into food problems.
People are poor because they're incapable of the value provision required to not be poor. This can come down to a number of causes: low intelligence (perhaps due to malnutrition as a child), discrimination, mental health issues, disabilities, geography, attitude, education, etc.
But it's scarcely a question of power. Centrally it's about capability to provide value to others who can reciprocate with money.
This is the premise of the EA proposal that you're missing. If I get a job as a software engineer, this in itself has value to society even if I don't wish to donate any of the money, since I'm being compensated for value provision to someone else (who is in turn being compensated for value provision). The EA on top is just a nice bonus.
Now, negative externalities are of course a real thing, and they need to be taxed so that payment for services is more correlated with true value provision to all stakeholders.
The problem is is ultimately the concentration of power (in whatever form it takes, money or otherwise) in the hands of a few. EA claims that doing more of the thing that causes these huge problems like hunger and homelessness will actually somehow cause less of it. And if you think I'm being reductive, fine, but I would ask that you point out what I'm reducing and why it shouldn't have been.