Dehav Driver, dont let economics get in the way of the real reason why the Engineers are on the headphones. They are not there for the 99% of pushbacks that are done without incident, they are there for when you have a problem on start. Imagine, "Cockpit to ground, we've got a hung start on number three." "Yep, the bags are on, you are good to go!" Comes the reply. Or the miriad of other technical problems that engineers deal with on start, that the tech crew, and no doubt the baggage handlers dont have a good working knowledge of. In my experience, the engineers save companies countless hours and thousands of dollars by avoiding un-necessary delays by suggesting "Fixes" to problems, not only prior to start, but during start and taxi.
Fellow drivers, how many times have a good engineer suggested a fix to a problem that is not "In the Book", but has saved massive delays and problems? No doubt, countless times. Engineers by nature look for fixes in the safety of the hangar, that pilots wouldnt dream of trying, for no other reason than there is not enough system information available to them (for good reasons) to attempt anything that is not in "The Book". If the MEL says "park it", it would be a very brave/stupid ramp guy, or pilot that would suggest otherwise.
Any company thinking of replacing this invaluable resource with anything other than appropriately trained engineers will do so at their own peril. It wont take to many potentially un-necessary delays to cost them a hell of a lot more than they will save by replacing them with a cheap operator trained in only the pushback procedure. Those guys on the other end of the headset are worth their weight in gold when you need them... The idea of calling the engineers on company frequency instead doesnt hold any water either. Much better to have a guy (or gal) on the spot, who has a first hand view of what is going on, did you ever play "Chinese Whispers" as a kid?
But, opinions are like @rseholes, everyone has one, just dont pick at mine...
