While it seems like this could be true under some circumstances, I don't see how or why this would be
inherently true. (Also, picking "billionaires" as the standard here is a strawman; GP didn't say anything about billionaires.)
1. Each billionaire wasn't created by a small EFT from every adult, so there's no reason to expect that reversing the transaction would somehow fix the issue.
If we focus on where the money came from (we don't try to solve for individual billionaire-creating events like inheritance), I would imagine most of it can be described as accrued by extracting small slices from a great many individual transactions (including labor arrangements, government contracts, B2B, retail purchases; directly and transitively through investments, incentives, etc). Little slices of the value that transaction may go to a very large number of individuals, institutions, and corporations.
A great many things seem plausible. Billionaires (or anyone that, as GP said, reaches material escape velocity) could be getting richer by obtaining ever-shrinking slices while facilitating an always-growing number of transactions. Or Billionaires might be growing richer by "winning" (concentrating) slices that used to go to a larger number of people near the top of the wealth scale (via competition or consolidation). Or they could be obtaining slices that used to go to everyone else.
2. While I think I agree that the big benefit of solving wealth inequality is clamping the range of influence, I'm not sure what magical firewall limits the influence of the rich to politics (unless you have a very expansive view of the political).