Demand incorporates/expresses value (fairly obviously).
Only if one uses circular logic when defining it, which is I find the MBA style definition of value to be mostly meaningless and also misleading, because people interpret it as they want. By contrast directly speaking of supply/demand encompasses everything quite well and eliminates any circular logic, let alone the need for such.
How would the demand curve avoid expressing anything the value the buyer receives (or at least perceives) from their transaction?
It doesn't. It simply makes clear that the reason is not 'value', as somebody might interpret it, but scarcity. If there were 100 million competent software engineers in the US, the value they add to companies wouldn't change, but their labor costs would - quite dramatically. In such a scenario coding and flipping burgers would offer relatively comparable wages.
Supply:demand makes the reason for this change completely clear, vague notions of poorly (and often circularly) defined 'value' do not.
For a more realistic example - the software side at many companies essentially is the company. They bring products all the way from inception to launch. Yet they tend to get paid less, often much less, than the legal side. The reason is simply that the labor pool for lawyers is much smaller than for software engineers.
If there's not significant barriers to entry for prompt engineering, wages will naturally be low.