As a sidebar, it is Interesting to note how quickly discussions about site selection for the US Amateur (particularly on this website) are rarely about the course itself, but about the logistical issues of hosting so many people, i.e. the companion course. The whole process is rarely about golf, or the merits of the design (which in this case is strong), but about the nature of business.
What "business" aspect is there? You have to play host to over 300 entrants for the stroke play qualification rounds. At a club with only one course, another course is needed, hence it is a natural question to ask when told that Riviera will host the championship proper.
Kevin,
It is a business when there are approximately 7,000 applicants each year who pay a $125 entry fee for the opportunity to play, totaling nearly $900,000. Moreover, I imagine that the USGA does not unilaterally select locations for championships; the host course(s) negotiate for the privilege to host. The results of hosting the tournament are symbolic (which has its own set of impacts) and are certainly financial. Monies are also often spent on course renovations in preparation for the tournament, which has potential downstream effects on construction companies, fertilizer and chemical companies, and certainly on-site maintenance labor, among others. And even for the Amateur (and to an exponentially greater degree at the Open) there is also an array of concessionaires working during the week of the tournament, on and off-site. Thus USGA events, even the smaller ones, are boons to local economies.
Also, what you mention in your post assumes that one HAS to play host to over 300 competitors. There is nothing "natural" about it; it comes across as almost arbitrary. But it's a conscious decision; no one has a gun to the USGA’s head forcing them to allow this many people to compete during the stroke play portion of the event. And whereas I certainly admire the USGA for making the gesture to the “open” nature of the championship, that anyone with a 2.4 handicap or less has a chance to win, I would think that an analysis of the history of the event probably suggests that true dark horses (e.g. someone with a handicap over scratch) rarely win, or are even found in the last few rounds of the championship.
Ultimately, though I don’t have proof one way or another, it seems logical that economics/business plays a determining role in the selection of a primary host course, as even the number of players in the field, which then compels the logistical necessity of a companion course.