This model predicts much higher prices overall than actually observed, especially on the goods deemed most essential (like food). There are many reasons that companies cannot simply charge "what the market will bear".

You’re mixing up two different questions. "What the market will bear" is a monopoly pricing story.

Food is messy because it's a commodity with a whole lot of substitution-- consumers have a high elasticity as a result.

We are talking about elasticity's prediction for the share producers and consumers each pay when there is a cost structure or tax change. Incidence theory is well validated and fits observed evidence remarkably well, including in 2019 studies of the effects of the 2018 trade war.