Manx

Those are not advantages afforded the non-rich. Those are supposed to be equal trades - a rich person gives work to a non-rich person, in exchange, the rich person collects most of the profit for the labor of the non-rich person. What I am referring to are true advantages - things that rich people are able to do that non-rich people are not, and in the process only the rich person gains. Most specifically I am referring to political power. Money buys political power (in the U.S. we mainly call it lobbying, in other countries we call it bribery - that way we can pretend that we are not, in fact, the most corrupt nation in the world). The political system of this country is managed by rich people, because they can afford the costs of "membership". In exchange, the non-rich people are given a "voice" via the lowest-common denominator producing election system. Non-rich people are given a choice of vicariously electing various rich people (now, there is the rare occasion where a non-rich person becomes elected to a position of ample power, but this is the exception, not the norm). The rich people then set the agenda, enact the regulations of the society and produce the media that the non-rich people consume to determine the "facts" they use to elect another rich person. This incredible power disparity is not effectively offset by higher taxes for the rich, but this power disparity must be included when discussing what is "fair" and what is not in regards to paying for our society.
For all of the above. And additionally, I do not see the overall mechanism by which all taxes would drop - you have mentioned various assumptions of explosive growth eventually rising from a consumption-based tax system. I am not sold on those assumptions. So, I see the system as nothing more than an almost 1 to 1 shift of taxation - $1 goes back into the rich man's pocket while almost $1 dollar comes out of the non-rich man's pocket. But even if we make your assumptions on growth, that still does not address the power disparity brought about by the progressive wealth structure of a capitalist society.
I would be open to addressing the power disparity of capitalist systems via other methods besides a progressive tax system. If there is some way of muting the power disparity while also flattening taxation, I would be all for it. I firmly believe in working hard to earn your way through life. But since the cards are stacked in favor of the rich - beyond simply the money aspect - I cannot ignore it by focusing solely on the financial aspect. If you are closed to investigating deeper into the needs of a socialistic remedy to power disparity, then there is not much more to discuss.
In that case - what we have now has been working for decades. Maybe with some minor tweaks here and there it will be fine for decades and decades more. Why throw it all away if all you're looking for is the success we have already proven?