It also shares with the direct estimation of the CES production function a number of other possibly strong assumptions: only capital and labor services enter into the production of real value added, capital and labor are homogeneous, the elasticity of substitution between capital and labor is constant, and capital and labor services are proportional, respectively, to capital and labor stocks.
Another reason is possible omitted variables, a topic discussed in section 4.3. The advantages of estimating elasticities of substitution between capital and labor from the ACMS forms are several.