This is all downside for no upside. The stated problem to solve -- that it's hard to fit search criteria into query string parameters -- is not really any sort

This is all downside for no upside. The stated problem to solve -- that it's hard to fit search criteria into query string parameters -- is not really any sort of real problem in practice. This would have us forgo cacheability, forgo the ability to send a link to a search, introduce more complexity into web servers and clients, all just to be able to send query parameters in the request body.