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A holy avenger won't get you that far with helping the poor. A few families at best. Better to use it during a full career of saving multitudes.
Throwing money at a problem alone is rarely enough to actually fix it. At best you end up treating the symptoms and not the problem itself, and at worst it makes things worse. You really need hard work, community cooperation, and good planning (and yes, also money) in order to really solve such problems at their root.
You misread what your link stated. 2000 is for a quality stone home. It's only 300 gp for a comfortable wooden house. A holy avenger is 2500 gp, that's fifteen families set up in comfortable homes for life. (Or half that if you are selling it, I suppose, but 7.5 is still more than a few.)
That also assumes you are taking the easy way out, of course. If the paladin put in the hard work you mentioned with their legendary diplomacy, connections, and reputations, they could instead rent a bunch of homes for even more families while working towards getting them sustainably employed. Get their druid friend to cast Plant Growth to boost their crop yield and what not. The whole "don't just treat the symptoms" narrative feels misleading because symptoms still kill people and get treated by doctors to prevent it, but there no particular reason a high level paladin needs to settle for that.
You can defend it, but its really just the "Reed Richards is useless" trope. We want to tell stories of fantastical heroes that can solve problems far beyond our own to make ourselves feel better about all the problems we can't solve. But because we want to keep telling those stories and we want the world to be recognizable and relatable, the heroes can't solve those problems for us. Pathfinder, much like Marvel comics,,has a vested interest in maintaining a status quo so these stories can keep getting told. Both also have geographies bot...
It's more the Batman problem, where we assume the billionaire could do more by spending his money on social improvements than on expensive tools to help fight crime dressed as a bat.Which sounds great until one of the villains destroys the city or something because Bruce is building houses instead of bat-gadgets.
In Golarion, paladins are paladins to fight great evils in a world full of great evils. If you fail because your equipment is up to par, things can get far worse, even for the poor.
Which doesn't mean that paladins, when not facing a crisis, wouldn't help in other ways, just that selling off their gear wouldn't be the best approach.
The other question is who would you sell the holy avenger to? By this argument, other paladins shouldn't buy it. Anyone who would can't be trusted with it.