Specialists are available in the second round. You know your team is weak under the boards? Take the guy who led the country in rebounding, like the Utah Jazz did in 2006 when they selected Paul Millsap No. 47 overall.
At the time, all Millsap was able to do was rebound and finish at the rim, but since his specialty was able to translate, he served a purpose on the floor. He was given valuable minutes early on, and in time he grew as a player and expanded his game.
If you can find a contributor in the second round, even if it's only in one department, go for it. Cheap rotation players don't just grow on trees, and the second round is a complementary tree full of potential reserves to choose from.