It's cool for the fairway on a short par-4 to be wide, sometimes. But not all the time.
Think about the best short par-4's you can. I'll name a few from my favorite courses:
Crystal Downs 5, 7, 15, 17
Pine Valley 2, 8, 12, 17
Merion 1, 7, 8, 10, 11
Cypress Point 8, 9, 13
St. Andrews 3, 12, 16, 18
National Golf Links 1, 2, 14, 17
Pacific Dunes 1, 2, 6, 16
They certainly aren't all tight, tree-lined holes, but they aren't all wide open, either. I really like the set at Crystal Downs. You can try to take a driver and smash it up close to the green but you can get in real trouble on all of them if you fail; and if you lay back there is topography in the landing area, so if you don't hit your tee shot solidly you have a tough lie for the pitch shot.