Total government tax revenue is about 32% to 33% of GDP.
fy2020 Federal: $3.65t; State: $2.1t; Local: $1.4t
Out of an economy roughly $22.x trillion in size for fy2020.
Those all must be counted as they each provide useful, typically different, government services at various levels and are paid for via taxation.
Total government spending is equal to about 37% to 38% of GDP (throw an extra trillion x in spending on the Federal number). This figure in particular is much closer to being aligned with typical OECD developed nations.
The deficit spending up at 37-38% comes out of American pockets one way or another regardless of taxation, via future currency debasement, QE infinite.
A VAT is a horrific idea and is wildly regressive. The very, very obvious tax change the US needs to make is also very simple: raise taxes on the top ~25%. And particularly raise taxes by a lot on the top 10%. There's absolutely no need to introduce a VAT when the US system is already perfectly well set up to boost taxation by a lot through its existing levers and the US system has immense slack income taxation potential. In most of the US you have to make around $600,000 to $700,000 per year before your total tax rate hits 40%. You can go make $5m, $20m, $60m per year and stay around 45% (higher in CA, NYC, etc). That's obviously going to change in the next 10-15 years.
As far as a VAT goes, you could adjust the VAT to fall heavily on certain items, but in many ways you're right. My point in that statement was to find a way to tax large corporations. I don't think the US tax code is "perfectly set up to boost taxation" when one of the largest growth sectors pays such low rates. Also the top 25% already pay quite high tax rates, and this option is also politically infeasible at least right now.
Moreover elites will continue to assume that demographics will eventually solve this problem, and continue to be disappointed when this doesn’t come true. All you have to do is look at slowing immigration in the US and how previous Democratic constituencies continue to switch towards the populist Republican messaging.