It turns out that market design can be liked by everyone from socialists to libertarians.
Here's Friedrich Hayek anticipating the subject, in The Road to Serfdom:
“There is … all the difference between deliberately creating a system within which competition will work as beneficially as possible and passively accepting institutions as they are. Probably nothing has done so much harm to the liberal cause as the wooden insistence of some liberals on certain rules of thumb, above all the principle of laissez faire.”
“The attitude of the liberal towards society is like that of the gardener who tends a plant and, in order to create the conditions most favorable to its growth, must know as much as possible about its structure and the way it functions.”
both quotes are from p71 of this edition, which you can search
And here's the Socialist Party of Great Britain (on the occasion of the recent Nobel economics prize for market design):
"As socialism will be a non-market society where the price mechanism won’t apply to anything, the winners’ research will be able to be used for certain purposes even after the end of capitalism...
"No doubt it would continue to be used to allocate organs to transplant patients and students to rooms. In fact, this last could be extended to allocating housing to people living in a particular area. While they may not get their first choice, people would get something for which they had expressed some preference and that corresponded to their needs and circumstances.