The bottom income/wealth deciles should definitely welcome price transparency, unless they are "temporarily" embarrassed members of the upper income/wealth deciles.
Efficient markets assume an infinite amount of indistinguishable goods sold by an infinite amount of producers with only marginal costs. This theory is useful because in many situations (e.g. commodities markets) this is a reasonable approximation. That is very different from how labor markets work, even in theory. Labor is not a commodity, there are heavy fixed costs (the costs of skill acquisition), and search costs dominate labor markets.
It is the whole reason why top down control and fascism or communism or Stalinism or Maoism are not ideal, because there is no better signal of supply and demand curves than prices.
The way prices move, over a sufficiently large dataset, indicate the way supply and demand curves are moving, and where the ball is moving so you can get to where the ball will be.
It is not perfect, of course, but it is better than the alternative (which is?).
Indeed, worrying about the efficiency of labor markets is a mug's game. We should be worrying about creating productive ecosystems and acquiring skills, and leave the labor market to be inefficient.
Here is a real world example I know from someone suffering due to their lack of interest in real world prices. Pay for most pharmacists has been flat since 2011, and declining since 2016. This is known from pharmacist sharing their pirate offers on pharmacy forums.
However, 22 year olds entering pharmacy school were not paying attention to this information, and instead were relying on the BLS's predictions that pharmacy demand would go up 10% and the schools' marketing showing that even though they will spend $200k on tuition, they will come out with amazing pay.
Now, if you read the forums, they are full of pharmacists regretting going into pharmacy, being crushed by hundreds of thousands of dollars of debt, and not doing their jobs properly of double checking prescription medications in order to ensure they still have a job because they have that student loan debt gun to their head.
So due to lack of pay transparency, there are tens of millions of Americans going to CVS and Walgreens getting medications from overworked pharmacists who themselves admit cannot properly vet the prescriptions to the degree they should. In the meantime, the schools that inflated tuition and class sizes got to benefit and taxpayers are left holding the bag by subsidizing these student loans.
Norway has had public tax returns for a long time.