I want to know whether or not a journal that published a proof $P$ of an important theorem $T$ is still open to accept another proof $P'$ of $T$ such that $P'$ is greatly simpler than $P$, assuming, of course, that $P'$ is correct.
I guess it depends on many things. First of all, what is the relevance of $T$ in its field? And secondly: what is the relevance of the new proof of $T$?
In my field of research, nonlinear PDEs, it frequently happens that a researcher can solve a PDE by a "new" approach. However, this approach might be confined to that particular equation, and a referee may decide that the publication of a paper with a new proof that applies to a single problem is not worth.
But it also happens that a researcher introduces a new method that can be used to prove (hopefully in an easier way) some known result. If this method is fairly general and can be applied to other problems, then a referee will probably accept the manuscript for publication.
Finally, more and more journals recommend to their referees that manuscripts should be original. A different proof of theorem $T$ will then be rejected almost immediately is the manuscript is written only to show that you found another proof.