Many underdeveloped countries had "small" 1 brigade sized divisions (some still has), and there are many reasons for that; when you have a small army and a big country to defend, it just makes more sense to have 6 1-brigade sized divisions than 2 or 3 full sized ones, it is also cheaper to build and maintain, while still giving some credible deterrent.
I think that China used 1-brigade sized divisions but I a not 100% sure.
Anyway, I am completely sure than many Latin American countries did. One example, during the short Peru-Ecuador war of 1941, Peruvian 1st Light Infantry Division was composed of:
1st, 5th, 19th Infantry Battalions
1st Artillery Group (8 guns)
1st Engineer Company
1st Antiaircraft Section
This should be a 1-brigade division in HOI3 terms
Finally, if the game is capable of handling a 1-brigade size division, and I want to play a minor country, I don't see any reason why I have to be forced to build 2-brigade sized divisions