Sorry but I have quite a viscerally bad reaction to such a proposal. Sure it could work in some sense of finding value price pairs or whatever where people's preferences aren't clear.

But it also seems extremely dystopian and horrifying, particularly applied to the dating market. It would be similar with finding friends. People do this naturally and normally on their own for free no problem if you put them in a big room together. It neeeds no incentive

I dunno. I kinda look forward to the news stories about the Economic Collapse of 2035 being due to the market finally realizing that too many supposedly AAA Date-Backed Securities were actually Non-Investment Grade Junk Dates, and the subsequent revaluation of the Date Market caused the entire banking system to become insolvent because all the dates they were holding on their books as marked to maturity are in fact never going to be anything but immature, and consequently must be marked down to their actual market value of Zero.

I mean, it's a pretty realistic economic threat. Who doesn't have a story of something they anticipated being a AAA Rated Date turning out to have junk date status? Definitely a lot of mismatched incentives all the way around.

I think you just reinvented sex work, but somehow made it more icky?

The main and big problem with this if anyone would consider it for dating for real, which probably they wouldn’t so no big worry, is what is in the price? So A just paid 20 dollars for the pleasure of having a date with B. What did A buy? Does B have to stay at the date for a set time? Is B obligued to listen enthusiastically to A? Does B have to laugh at A’s jokes? Even if they are lame? And then of course what happens when A thinks they paid for sex and B thinks not?

Or possibly expensive engagement/wedding rings in non-jewellery form.

On a separate point, some of my socialist (and in a few cases literally communist) friends assert that the issues at the intersection of sex work with consent also apply to all other work under capitalism; I don't have a strong counter-argument to this.

Money is fundamentally unnatural, so it's not surprising that it feels wrong and icky in a lot of situations.

I think that is only sometimes true, usually in situations where relationships are mainly economic decisions. As prosperity increases and pay/power differences between genders shrink, it is becoming less frequently true, and less true on a per-relationship basis, over time.