If we brought down Chevron, then BP and Exxon would cheer, since they'd have one fewer competitor.

The problem can't be resolved (or even really mitigated) by targeting certain people that we think are more "greedy" than others. Because the underlying problem isn't really a human problem at all - the universe has greed built into it. Black holes are greedy for matter, large trees are greedy for sunlight (and block out the understory), empires are greedy for land and resources, etc. Greed, AKA power aggregation, is one of the most inescapable patterns of the universe.

We can sometimes create subsystems (e.g. a family or a small community or company) with different rules than the universal rules (e.g. greed / power aggregation), but those subsystems always have to be able to survive within the larger universe, where greed and power aggregation are the inevitable norm.

The big problem with capitalism today isn't greed (which is not new, but eternal and ubiquitous), it's globalization, which is enabled by technological advancements in transportation and communication. The local tribal leaders of bygone eras only exercised dominion over their small village and nearby territory, whereas a large business today commands resources around the world. And that creates larger disparities than were previously possible.

So rather than trying to solve these problems by demonizing and attacking certain "greedy" people, we're more likely to see some success simply by fighting globalization in general. And we can do that by adopting practices and technologies that encourage distribution, rather than aggregation, of power.

For example, solar power can help put energy production in the hands of individual homeowners, rather than big energy companies. And vertical farming might allow crops to be grown locally in more locales, rather than forcing people to import food from faraway mega farms.

The best way to disempower the rich is to need them (or at least the things they control) less. And the way to do that is to figure out how to feed, house, and clothe ourselves locally, rather than globally.