Great question. Your situation is a sort of "glass is half full, half empty".
The glass is half full, the reviewer cares a lot. The glass is half empty, the reviewer cares a lot.
Perhaps you are in the situation where the reviewer agrees that the paper is acceptable though with a different analysis. There is no obvious (to me) harm in doing the reviewer requested analysis. I happen to have done a lot of work with PRO's (patient reported outcomes) and with Likert scale. Psychometricians have very specific ideas about analysis and more specifically for the connection between actual human behavior and the statistical models of that human behavior, and broadly divide their philosophy into 'classical test theory" and "item response theory". Caveat Emptor, You do not need not take a deep dive into psychometric theory for your specific paper.
To more directly answer your question First it would be helpful to have a definition of the metric ordered probit model. I may be wrong, -I think Jackman has written thoughtfully about these models.
https://web.stanford.edu/class/polisci203/ordered.pdfyour citation to Liddel Kruscke also gives a not-too-technical definition of metric ordered probit models.
I would be (prepared to be ) surprised if your non-parametric method and the reviewers choice give markedly different answers.
It looks like (after my -lite- reading) that the metric model has a few more "bells and whistles" that psychometricians view with fondness.
If one analysis (subject to caveats that follow) is all that's needed, to get the publication, then I'd recommend doing that -again with caveats below.
One option (you have several ) is to agree to do the reviewers analysis as an appendix and present yours as the preferred analysis, given "all the very well known limitations" of the metric ordered model. This is the "do it both ways" approach and there is no guarantee the results are the same nor can I guarantee the editor will accept it. . My caveats and my personal "line in the sand" as a reviewer. I generally require that the following are true. First I require that authors state their analysis was "pre planned" and my second line in the sand is that the authors gave appropriate "consideration to multiple comparisons".
Entirely separate , I would personally be interested to find out if the two approaches yield similar interpretations.
------------------------------
Chris Barker, Ph.D.
2022 Statistical Consulting Section
Chair-elect
Consultant and
Adjunct Associate Professor of Biostatistics
www.barkerstats.com---
"In composition you have all the time you want to decide what to say in 15 seconds, in improvisation you have 15 seconds."
-Steve Lacy
------------------------------