Divisional level actions were standard for 1919 and 1920 across the war. They did have small divisions, and some of the White Brigades were the size of a Soviet division, but the intention was almost always that the manoeuvre element was the division or reinforced brigade.
Other than a few places with closed terrain, it would have been quite dangerous for a small unit to operate on its own near opposition with brigades of cavalry.
Smaller sizes were only the norm in 1917 and 1918, before the armies started to grow.
The Polish war in 1920 wasn't particularly different. They packed them in a bit around Warsaw and Ciechanow, but less tight than around Petrograd, Tsaritsyn or Kakhovka. The battle of the Nemen was the second biggest of that war, but extended over a massive front. (I would guess that the densest fighting was Perekop in late 1920 and Narva after the end of the Petrograd operation.)