First time I've heard of pros and cons on this subject. VOR procedures have had system tolerances (flight technical error) evaluated and procedures developed over the years on the premise that the course deviation indicator CDI would be used for radial tracking.
RMIs have issues that make them suitable for reference but not for VOR radial tracking.
If you routinely use your crosscheck and backup instruments, then you will not be looking at an unfamiliar panel or struggling to even set it up if your primary instrument fails. I have flown (and been evaluated on) MANY VOR (or TACAN) and NDB approaches, including to aircraft carriers, using only an RMI for course guidance. It can be done within approach tolerances if you practice regularly.
It is no different than the automation/hand-fly argument. If you think you NEED an Autopilot or Flight Director or CDI or HSI to fly the approach, then it is likely you will not be able to to fly one without the instrument. OTOH, if you practice regularly in ALL available modes, then a simple instrument or system failure will not turn into an emergency procedure...