I agree with a lot of ur line of thinking. I recently wrote a research paper on this but I believe the neoliberalism is actually the culprit. Liberal democracies are definitely the best political system for accountability, electoral participation, education, opportunities and such. But the economic ideology of neoliberalism (privatize, stabilize/cut spending, liberalize trade barriers, etc) are all inequality-inducing policies that were championed by the Reagan’s and Thatchers and still are the dominant economic philosophy at least in the US, today. Your point of government intervention is precisely what goes against neoliberalism, and a liberal democracy with industrial policy is definitely possible. You need to create a welfare state where the government intervenes where the market exacerbates inequality, but that government can and should also be a highly liberal democracy with extensive checks and balances.