I think you miss my point. Even if the tax rates are the same, a state with a larger GDP - whether that state is South Carolina or Singapore - will have more money to spend on things like health, and government, actually, just everything - thats's why a higher GDP is so desirable.
An ambulance in Singapore can pretty much reach anyone. A hospital in SG can server anyone - that's how small it is. Who serves Idaho? The Mayo clinic? In a roundabout way yes, but not really.
Quoting US statistics and comparing them to SG is analogous to comparing the same statistics in the Bay Area and Miami.
And that all this gets wrapped up into one single country metric obfuscates the true state for most people, and leads to a lot of problems as one group struggles with a smaller, yet more visibly lacking, share.
If you are poor, however, forget about it. Those states are openly hostile to you and generally opt to find the minimum number or services allowed by law. They are so bad that many people establish false residency in states with better systems.
The way these programs are funded, it makes little difference to state balance sheets — it’s all about appealing to particular political bases, and keeping certain taxes (typically property taxes) low to keep the old money people happy.