MV is one of the top 10 courses I have ever played. Why it does not seem to be held in high esteem on this site may be because: 1) it was done during a period of time when many here thought that architecture was in the dark ages; 2) Jack Nicklaus rubs some people the wrong way; 3) its reflection of $$$$$$$, and, to some, over-the-top "Augusta syndrome" maintenance; 4) that most participants here have neither seen the site nor played the course.
For the average player, MV is way too difficult. Don Claypool, a former Columbus insurance executive who became the caddie master at MV upon retirement, told me many years ago about a group of well-heeled Japanese businessmen who jetted in for a round. Apparently, they each loaded-up with a dozen balls, and after an hour or so, somewhere in the middle of the front nine, they all came in for a resupply.
The course is unrelenting; even the "easy" par 5, #15 can come up and bite you in the butt. Never have I seen water hazards that really come into play as well as they do at MV. Well hit, solid shots on the wrong angle are sometimes punished severely.
And the greens are something else. During a district open tournament, I somehow found the fairway on #1, hit my second with a middle iron to within 20' of the hole, then proceeded to hit my first putt 30'+ past, the next one 4' short, my third (shaking) 1" short but on-line. I had an extremely long day (6 hours, and barely broke 90; the medalist was the head pro Jim Gehring with a 72 who then got disqualified for using a towel to sweep sand off a green; and something like 83 made the first day cut). Amazing, but over 25 years later, I can remember every hole and most of my shots vividly (I sometimes have a hard time remembering my telephone number).
I don't really know Muirhead's style to comment on his involvement here. I have played numerous JN courses, and I can definitely see his imprint. A criticism that I would have about MV is that it does not allow enough for the ground game. It seems to greatly favor the high lofted, soft landing shot. The course also has great topographical variety and a very nice mix of holes. One definitely has to think his way around it.