This is not that unusual. I know in St. Louis, that St. Louis CC, Bellerive CC, Old Warson CC, & Norwood CC all have the pro shop in stand alone buildings. I also know that at Algonquin GC (also in St. Louis), that the stand alone building that is now the bag room, caddie house, and cart barn; was many years ago (>40) also the pro shop.
St Louis CC recently (last 15 or so years) built a new pro shop, next to where the prior pro shop used to be. Both the prior and the current are stand alone.
In Longmeadow Ma, Longmeadow CC also has a stand alone pro shop.
I have no idea why each of these facilities chose to have the pro shops in stand alone buildings. However, one of the pluses is that the pro shop can be more easily kept open when the clubhouse itself if closed. In St. Louis golf can be played year round, including in Jan & Feb when some country clubs shut down the clubhouses for a few weeks for updates and renovations.
At St. Louis CC & Longmeadow CC, the pro shop is right next to the first tee.
At Norwood CC, the pro shop is right next to the driving range.
At all three of these facilities, the bag room is also housed in the same building as the pro shop, and cars can easily drive right up to the bag room and drop-off/pick-up their clubs.