I have worked and visited facilities that have had their golf shops in their main clubhouse as well as a separate building. I have played 214 courses (all in the American Midwest, Northeast, Middle Atlantic and South), and only 36 of which have had separate buildings for their golf shops (see list of those examples below). Of those on my list, they are overwhelmingly in the Northeast and Middle Atlantic. I suspect thats the case for one main reason: age of the facility.
As others have mentioned in this thread, many years ago, many golf professionals owned their own golf shops and paid their own employees, and were allocated space in a separate building to run their operation. There are exceptions to that rule, Im sure, but if I were a betting man, I would say that is why so many more that I have experienced have been older clubs on the east coast. Furthermore, a quick analysis of my list below shows that while some have expansive main clubhouses, many are smaller and others have been added to over the years, leading me to believe that the golf shop was not a huge priority for member clubs years ago. Lastly, some who have separate shops have utilized existing buildings that are converted into clubhouses, such as old barns, and it may have been easier to build separate golf shops rather than adding on to and retrofitting an existing building.
In my personal opinion, there are probably more cons" than there are pros to a separate golf shop, but others may disagree with me. A separate golf shop could mean the club staff and the golf staff operates more independently, rather than presenting a unified front, image and brand.
American Midwest and South
Arlington Richmond, KY
Browns Run Middletown, OH
Camargo Cincinnati, OH
Hyde Park Cincinnati, OH
American Northeast and Middle Atlantic
Bala Philadelphia, PA
Bluestone Blue Bell, PA
Buck Hill Falls (PA)
Center Square Norristown, PA
Elkridge Townson, MD
Glenhardie Wayne, PA
Harkers Hollow Phillipsburg, NJ
Hayfields Hunt Valley, MD
Hollywood Deal, NJ
Huntingdon Valley (PA)
Jack Frost National Blakeslee, PA
Lebanon (PA)
Llanerch Havertown, PA
Lookaway Buckingham, PA
Meadowbrook Huntingdon Valley, PA
Mount Airy Mount Pocono, PA
Oakmont (PA)
Old York Road Spring House, PA
Paxon Hollow Media, PA
Philadelphia Cricket Flourtown, PA
Phoenixville (PA)
Pocono Manor (PA)
Rehoboth Beach (DE)
RiverCrest Phoenixville, PA
Rolling Road Catonsville, MD
Scranton Clarks Summit, PA
Somerset Hills Bernardsville, NJ
Spring Mill Ivyland, PA
St. Georges East Setauket, NY
Sunnehanna Johnstown, PA
Timber Trails Pocono Pines, PA
Youghiogheny McKeesport, PA