Holding committee seats can sometimes suck! So majority coalitions should keep just enough committee seats for itself to be able to maintain control

Legislative committees have substantial power over the legislative process. Most enjoy negative agenda control—meaning that they can prevent any bill from moving to the floor and receiving a final vote—and nearly all have considerable authority to rewrite bills. Because committees are so influential to shaping policy and influencing outcomes, political scientists typically think of committee seats as strictly “good” and implicitly think that having more is always better for a legislative party than having less.

It may seem strange, then, that majority coalitions in legislatures do not just keep all committee seats for themselves. Why give minority members any access to influence at all?

Our article, “Allocating Costly Resources in Legislatures,” makes a point that most legislative research has looked past: committee service is time-consuming and this can make committee membership burdensome. Committees have lots of meetings (where absence is often punished) in which they sift through information, hold hearings, mark up bills, and take lots of votes. Some of this work can be passed off to staffers, but not all of it. While this work allows  committee members to exert policy influence, it can often consume time they would prefer to spend elsewhere—like performing constituency service or fundraising. 
https://doi.org/10.1086/717853