Good pitching is like good produce at the grocery story: fresher is better. Memories of the 2015 NLCS are proof to that fact. Further proof is in the numbers. The workload of these pitchers during the regular season affected their playoff performance. (See table below)
The eventual NLCS winning New York Mets had zero pitchers with more than 195 IP in the regular season. Bartolo Colon pitched 194+ innings but did not start in the postseason. The World Champion Kansas City Royals? Two pitchers with 200+ innings (Johnny Cueto and Edinson Volquez) in the regular season, but the rest of the staff was under 164.