There are reasons for both approaches.
Thirty years ago (!), when I started working at Garden City Golf Club, there weren't many clubs in America that would have considered a $3 million restoration [much less a $15m one]. Our work there and at Camargo and Shoreacres was done slowly over many years, because the clubs were quite conservative in their approach. While I had presented them with a long-term vision, the membership weren't "sold" on it at all . . . we did some work, they appreciated it and wanted more, and eventually we got there.
In that approach, it's important to start with the little things. Mowing lines, and trees that aren't too controversial. Then, identify a hole where they have a problem, and fix it. Transforming one hole to a "new" style can backfire entirely: if it's not received as a faithful restoration, it will just look out of place. I distinctly remember the first time I saw Bel Air, the 7th hole had been redone by George Fazio in the 70's, and they didn't ask him back to do the rest.
That approach has mostly fallen out of favor now. Greenkeepers are wary of the course "always" being under construction; they're also wary of losing focus on the turf because they are distracted by the construction. So, they'd prefer to hand off that responsibility to an architect and a contractor.
Once you're on a contractor's schedule, they'd prefer to get the job done all at once, instead of doing 1/4 of four different projects over 4 years. Most architects would, as well. It isn't better or worse for the result necessarily, it's just more efficient for business.