In a statistical model with parameters $\theta$ and unobserved laten variables $Z$, the model likelihood is

$$L(\theta;X)=Pr(X|\theta)=\sum_ZPr(X,Z|\theta)$$

The standard way to estimate $\theta$ is to maximize this likelihood (e.g. using EM or so). However if this estimation is computational intractable, can I maximize $Pr(X,Z|\theta)$ w.r.t both $Z$ and $\theta$, and use this estimated $\theta$ as the model parameter? Does this method have a name? What is the main drawback or problem with this method?