Pushing hands as a body conditioning tool in the chi-meditation system holds a very special place. First of all, it is not a solo system. And secondly one needs a partner who preferable shall have a higher degree of chi-competency. As far as body conditioning is concerned, the practice of pushing hands is optional. Having said that if one got a good sifu or coach (and has the discipline and the time), pushing hands can be a supplement to one's chi-meditation system.
The key training objective of pushing hands is to generate chi-flow and opening the student's ball-and-socket joints, mainly the shoulder joints. The first requirement of pushing hands is that the mutual force at the touching point(s), usually the hands or forearms, between the practitioners should be constant, with one side just minimally greater to facilitate a smooth flow (usually in circular movement simulating a form of close-range combat). The second requirement is that the force in the touching points has to be based and transmitted from the feet. These two requirements trained the practitioners to be at muscles-as-one (肌肉如一) even when in the form of motion and in contact. As such it is also a foundation practice for tai-chi as martial art. And it is therefore a pre-requisite that muscles-as-one has to learned from zhan zhuang (standing meditation) before one can effectively learn pushing hands.
From the above analysis, we can see that learning pushing hands is not compulsory for a complete system of chi-meditation mind-body conditioning training. And if combat is not your training objective, it is not necessary to spend too much time in learning pushing hands.
However, from yet another perspective, learning some pushing hands might be useful. I am talking about Healing. I have the experience of doing (passive) pushing hands and pushing legs with advanced age wheel-chair confirmed students to stimulate chi-flow and joint-opening with good results.
I have said previously that one needs faith (belief and humbleness) to effectively learn chi-meditation exercises (or practice), but I also believe a student has to know where he is going (like will take how long, what are the benefits, any side-effects) before he commits his faith to his coach. And his coach has the responsibility to explain. If your coach refuse to do so, I suggest you should seriously contemplating finding another one.
PS: I am talking about tai chi pushing hands here, but other styles of Chinese internal martial art, like I-style, also have their own form of pushing hands.