> Businesses don't raise prices to "keep margins the same"

It's absolutely common practice. A few luxury businesses can get away with outsized margins, but everyone else in the physical goods business is working at 60-70% gross margins (so MSRP is usually ~3x cost). Grocery stores are outliers with absolutely razor thin margins.

In twenty years in e-commerce, I've never not seen prices updated to keep margins in a narrow band.

The only thing that will happen is if you have multiple competing companies, they affect each other's prices in ways that may make the band wider. You also have the various x.99 prices that companies want to hit (so a grocery store will sell something for $4.99 and not raise the price to $5.17 to keep their margins, but will hold out until they feel they can jump to $5.49 or $5.99 - this right here is the biggest reason for "shrinkflation" - the price wants to move to something that is not a .99 and so they resize it to make it hit one.)

But no company will long run at a loss.