Because you almost always care about proportional changes not absolute changes. If you buy at stock a $1 and it goes to $10, you have made a ton of money. But if I then buy in at $10 and it goes to $20, I have merely doubled my investment. Logarithmic graphs convey this clearly. Linear graphs make our returns look too similar.

It is very common for inflammatory articles to use absolute numbers that (intentionally or not) ignore inflation, changes in GDP, etc... because it is both simpler to explain and more effective for inciting outrage.

?I don't understand why there would be a need for a logarithmic graph in this case. The author is not discussing proportional changes or even absolute changes, unless you want to consider income as a change in wealth, but that's not quite accurate and adds an unnecessary layer of complexity.

The author's main goal is to show how a proxy for decision making power (viz. household cash income) is highly concentrated.

I don't think the author's graph is the best visualization of his point. I would like to see a graph of the proportion of national wealth owned by households at each percentile. The would deliver the point the "power is highly concentrated" in the top percentiles. Wealth is a better proxy than income and understanding the proportion of wealth each percentile holds claims to is better than seeing the absolute amount of wealth held by that group.