Manufacturers aren't stupid and don't do impulse response. If they can tell the price shock is likely transient - that the demand will evaporate before they'll manage to ramp up production - then they won't even bother.
If they knew that every decade or so, they might temporarily be able to sell at 5x the normal price for 3 months, they’d likely run their outbound supply chain slightly less just-in-time.
Ironically, this might make things less likely to get to the point where the market price was 5x normal.
They run them less just-in-time that you think, e.g. 3M were able to double production in a couple of months [1]. I'd say that's pretty impressive, but what do I know. Regardless, preparing for these events is the government's job, including stockpiling the required PPE. In fact, in a bunch of countries the stockpiles were scaled down or simply never replenished because it was deemed an unnecessary expense (France, Belgium, Canada).
High prices also discourage some frivolous wasteful panic buying. People are going to miss out no matter what, but at least with price gouging, there's some sorting related to need, even if it's imperfect.