I have been reading several papers that use 2SLS. These papers usually also show the OLS regression results. I noticed that when authors report results for 2SLS, they also include control variables that were used in the OLS regression.
If 2SLS is supposed to solve the omitted variable bias, couldn't we omit the control variables that are included in OLS because we do not have to worry about omitted variable bias? For what reason would authors include those variables?