I suspect that JRiver's problem with ASIO4ALL is simply that it is third-party software, so it introduces an additional layer of problems. For example, the most recent ASIO4ALL release has a bug whereby the action of the 44.1<->48 option is the reverse of what the option says. This already caused a problem to be reported in this Forum that was not due to MC18.
In contrast, WASAPI has no third-party software, and so JRiver can just deal with the well-known details of the API, without any further "variables" being introduced.
As a programmer, I can sympathize with that.
I would rather that JRiver frankly say "ASIO4ALL introduces factors beyond our control, so if you use it, you are on your own", rather than just repeating irrelevancies about "wrappers" (probably less than 10% of the readers understand technically what a "wrapper" is).