I'd agree with 99% of the above. Pushing hands is a style of training that involves many, many techniques. It is vital to all the aspects of T'ai Chi Ch'uan. Without it, one cannot benefit fully from T'ai Chi's health, meditation or martial potential.

The 1% that I can't agree with (I plead ignorance!) is that I don't know William C.C. Chen well enough to comment. I've heard of him, that's all. If a school is incorporating any other style into their T'ai Chi curriculum, then I'd say that is a bad sign, however.

Pushing hands is a huge subject, very complicated. If you have a full pushing hands schedule you don't have time to study Western boxing! We have 12 different styles of pushing hands at our school, 8 choreographed patterns and 4 different freestyles. Eventually they lead to freestyle sparring (which includes wrestling). Along with the pushing hands we have two person and then multiple opponent application drills, empty hand and weapon. This is at least 10 years worth of work just to cover the basics!

As mentioned by delibandit above, many schools have lost such a thorough syllabus, teaching only one or two styles of pushing hands, if they teach any at all, and those one or two styles are uninformed by the rest of the pushing hands agenda and thereby incomplete even for what they are supposed to do.