I'll flip this around and instead elucidate when it does apply if that's alright.
The supply and demand model only applies to analysis of microeconomic systems with perfect competition, namely of systems that lack monopoly and monopsony; that have perfect information; that lack an ability of a single economic actor to affect the price in the market; that lack externalities[0]; that lack transaction costs; that lack unknowable probability distributions of outcomes; that lack economic actors that change their behaviors based on what they expect other actors to do; and that lack non-market rules or structures that restrict prices, quantities, or entry. These assumptions are all-or-nothing, and there are a lot of them. It's also an equilibrium model, and we aren't guaranteed to have equilibrium.
For macroeconomic analysis (i.e., analysis of multiple sectors of an economy or multiple economies), it's problematic because of a theorem from the 1970's due to Sonnenschein, Mantel, and Debreu. I've stated it elsewhere, but it also has the implication that the behaviors of the actors in a microeconomic system do not carry over to the macroeconomic context. This tends to violate many of the assumptions above. (Though, if it isn't obvious how or why, please ask.) Furthermore, in the macro context, I don't think we'll ever have equilibrium; at least, I'm having a hard time thinking of an example when it exists.
Let's bring in a physics analogy. While we can look at mechanics through the lens of elementary algebra, those tools really only give us the ability to look at static force-balance problems for springs and pulleys in equilibrium. To model such a system more closely to how it behaves in the universe, with damping, inertia, and feedback (and whatever other time-dependent behaviors I may be forgetting), we are best served moving to differential equations.
Economics is no different; the supply and demand model is a lot like Hooke's law in its simplicity and its applicability. (In fact, in my modeling, I very heavily used numerical solutions of PDEs.)
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0: When the retail price of kerosene tanked by 70% between 1860 and 1880, this resulted in millions more kerosene lamps and lamps broadly being lit for longer periods of time. This had externalities in the form of more soot and particulate matter (and probably also respiratory illness, but I couldn't seem to find anything with observations from the time period).