My understanding is that the US has so much more debt now than we did in the 80s that a rate hike of that magnitude would cause too much harm for the Fed to stomach.
The Treasury pays interest on government debt. The Fed does not. Raising rates causes the Fed no harm other than (a) risking recession and (b) creating accounting losses idiots politicise. (The same way the Fed's accounting gains as it lowered rates are a useful fiction.)
When the Fed raises rates, it increases the rate the U.S. pays on new debt. Over time the U.S. government's interest outlay would thus rise. But we're nowhere near that being an issue. To the degree it would be an issue, it would manifest as inflation. The specter rates are being raised to fight.
There is C: politics. It is believed that the Fed is directly responsible for Carter losing to Reagan. (though it isn't clear how the election would have gone otherwise, it wouldn't have been the landslide it was) The Fed also reports to congressional hearings.
The point being, they can try to kill it first time, or maybe they have to raise even higher later on which would be even worse for the problem you're talking about.
Also, they're on record as being fully aware of this.
> According to the Congressional Budget Office's (CBO) latest baseline, the federal government will spend $400 billion on interest payments on the national debt this fiscal year (FY). That's equivalent to just over 8 percent of all federal revenue collections and roughly $3,055 per household ... Interest costs and the national debt could be even higher if interest rates continue their upward trajectory and outperform CBO's latest economic forecast. Each one percentage point increase in interest rates would increase FY 2022 interest spending by $38 billion at today's debt levels.
As the interest rate increases, those payments increase also - this is money that is spent and doesn't "get us anything more" - it's just maintaining the current debt load. The site linked is obviously arguing for "spend less money" but the math checks out, and if the debt never goes down interest rates can have a major effect. (Now sure, some/most of this debt is paid to the government itself.)
A sharp increase in bond interest payments set off the Greek crisis.
Here is a simple example with made up (but not completely off base) figures. Assume US government has debt amounting to 100% GDP. Assume also that it collects taxes amounting to 20% of GDP. If rates are 2%, then interest payments are 2% of GDP, which is 10% of the budget. Now, if bond rates go to, say, 6% (current mortgage rates), then interest payments are 6% of GDP, which is now actually 30% of the budget.
Basically, at high debt-to-GDP ratio, small changes in the interest rates cause huge swings in how much budget is spent on interest payments. This money has to come from somewhere, and more debt is only a short term answer.