> Would it not make sense to set rates somewhere in that window (roughly 2-4%) and stop messing with them? For other countries, scale rates accordingly.

That alone wouldn't work because inflation is affected by factors beyond interest rates, but this is basically a part of Modern Monetary Theory: set short-term interest rates at a fixed price, then use other levers to push inflation back to target.

IMO, a more compelling alternative to the current system is Nominal GDP Targeting.[1][2]

[1]: https://www.mercatus.org/research/research-papers/case-nomin...

[2]: https://www.mercatus.org/research/working-papers/nominal-gdp...