Putting aside your misunderstanding of supply/demand elasticity, interest rates are set by the Federal Reserve. Top down controlled. Like in a Commie Country. Subjectively set based on their own goals. Not a side effect or a consequence.
Sounds like you took Econ 101 (Micro) as an undergrad and drank the Kool Aid.
Well, yes, I get that. Interest rates are set by a small group that has been delegated a monopoly control over them. The possibilities for abuse are almost unlimited.
The key discount rate is in effect an "off the top" commission that the central bankers take for their issuance of new currency (US Treasury Bonds). But changes in that base rate do not cause or prevent inflation. Changes do protect the central bankers from the effects of inflation. They are happy to cooperate with the US Treasury as long as they get their cut first.
What makes you so sure that I misunderstand supply/demand elasticity? I certainly remember the 1970's with rising interest rates, slumping economy, and rampant inflation. "Stagflation" it was called. The economists of the day thought that was impossible. They still maintain that it is impossible because it conflicts with the conventional explanations offered by the Federal Reserve.
Most of the explanations for inflation are designed to protect the people who benefit from it, and distract the potentially angry mobs who might otherwise object to it.
For that same reason, most of the suggested remedies for inflation are ineffective, self-serving,, or even destructive. ("Let's raise those loan interest rates again. But lets keep savings interest at effectively zero").