I think what you’re still missing, aside from the situation of the “wealth gap increasing” being a bit more nuanced, is that extreme inequality long predates corporations and capitalism. Therefore, using these concepts to attempt to explain it begs the question of what happened before.

Again, wealth inequality is primarily a consequence of the existence of markets, capitalist or not, corporatist or not. The modern market economy in fact allows societies today to much more effectively combat the issue. The Bible doesn’t mention progressive taxation, estate taxes and welfare states since those societies never had the administrative capacity to organize it.

Now, you can argue that current societies that do use these tools effectively (certain European countries) should increase the degree of progressivity of taxes, and I would agree. But it has absolutely nothing to do with corporations or capitalism directly. The influence of moneyed interests in these countries, while arguably still too large, is not anywhere near the overt bribery and naked corruption we can observe in the United States.