Yeah, the problem is that the "law of supply and demand" is a simple metaphor to help children gently begin learning economics, not how anything actually works. Almost no price any real person encounter anywhere in their daily life is actually determined in any meaningful way by "supply" or "demand" -- unless you stretch the definition of those two words so thin they're practically meaningless. They're potential factors, sure, but only small ones.
As one of a bajillion examples, see how every hospital is short staffed (low supply) and desperate for nurses (high demand), while we also see them constantly lay nurses off or reduce hours (and nursing has consistently-fixed low salaries, despite the shortages). Same for CNAs, nursing home staff, etc.