a progressive tax on profits linked to market share and niche dominance
I like the spirit of what you are saying which sounds to me like "let's increase freedom" or "let's encourage good corporate governance." Freedom and competence are good things, for sure. However, I don't agree that giving the government more power/reasons to rob folks is a good idea. Remember what the government spends the money on. They minimize the good stuff (roads, kids, local defense). They maximize the bad stuff like foreign wars, secret bio-weapons labs, experiments on the population, group-based biased transfer payments, overregulation of things they can't keep up with like tech and pharma, punishing the little guys while letting the big corps run wild, etc... The government is not the good guys that need rewarding. People who create goods and services that aren't harming society are the good guys, not a bunch of evil soon-to-be-tax-donkeys we should stifle.
The current tax systems seem to favor greedy monopolists.
That is true. It's also punishing individuals, the middle class, and based on the worst possible (most unjust) modalities of taxation: income robbery and property robbery. So, you can't keep what you earn and you cannot own any property because the government can take it the minute you stop paying them rent. The taxes (robbery) is bad. The way they collect them is worse. The things they spend the ill-gotten-gains on are the drizzling Hershey shits. So, the best option in terms of effectiveness and fairness would be to cut spending and radically reduce the size of our incompetent and murderous government.
Another involves the case of natural monopolies (often related to network effects), where one solution approach would be to use some of the tax revenue to regulate the natural monopoly while funding research into ways to break the natural monopoly.
I don't know where to come down on these types of network-effect monopolies. Part of me says "Well, Apple/Sony/MS built the walled garden let them live or die in it." However, that ignores how big these companies get and how powerful and large the market places start to become. The effect becomes so large that it might actually be at least worth considering letting the incompetent murderers help solve the problem, lord help us. However, I doubt it. I'd assert that in a sufficiently free market, network effects will get nullified by better and more competitive networks. If they don't (like say with Standard Oil) it might because the monopoly is being really well run and competitors cannot break in. General rules against fraud, breach of contract, or actual coercion still apply to walled gardens.
Your better ideas are quite welcome.
My ideas are more ideologically pure and probably would generate better outcomes (more freedom & wealth) if fully implemented, based on histories precedents. However, my ideas are also less realistic and less easy to implement than yours. Your ideas are at the "Let's radically change tax policy" wonk-level. That's bad, but it's not nearly as bad as "We gotta burn this system to the ground and start over with Capitalism" which is basically my idea. So, the merit of the idea depends on your goals & perspective.
Also questions triggered by my poor writing.
Nah, you're not being a smarmy trite shithead. There is no reason to be trite to you. I just usually match the energy of the parent post, ala Witroth and his "come out partisan guns blazing" crap. You want to have a discussion, just avoid the smarm and ad-hominem that's ubiquitous here and we'll have an actual conversation.