Sticky wages are the reason for unemployment. The standard academic explanation of this can be found here:
Unemployment is just a labor surplus; since wages are the price of labor, the fundamental cause of unemployment has to be excessive wages.
The fact that wages are an essential component of AD is completely ignored here. Suppose we cut wages across the economy. Following this, there are two possibilities:
(1) Prices fall. Real wages remain unchanged and all that happens is that real private debt increases and the money stock increases, the former being negative and the latter achievable with expansionary monetary policy.
(2) Prices do not fall. Profits and rents are increased by reducing wages, but that effectively means redistributing to the rich, who have a lower MPC. It would not be right to assert that consumption will always fall by reducing nominal wages, but it is fair to expect a drop. And in the face of this falling consumption, are businesses really going to invest their profits?
Number (2) rests on a lot of introspection and supposition. But the fact is that there are no examples in the real world of wage cuts leading to falling employment, quite simply because wages drive demand, which is what drives employment. Nominal cuts didn’t work in the Great Depression, and the period with sustained real wage increases (1945-1973) coincided with very low unemployment, whilst the period of stagnant median wages (1980-present) has generally coincided with higher unemployment.
And, of course, no, Keynes did not argue that sticky wages explained demand side recessions. He argued the exact opposite - that they actually help to nullify them. Sometimes I wonder if anybody has even read TGT.