"a not insignificant proportion of new recruits get the engineering training and then leave at the first opportunity ..."
I'm not sure what the waiting time is now to get out of the Army early, it It is a long time since I did so. But the reason I bought myself out wasn't the lure of civvy street and its better jobs, it was that we were given nothing constructive to do. I was in the RAMC which I believe has a recruitment problem, they certainly did when I was there. The trouble was once they had you they struggled to find something for you to do. In my case it was putting up tents for the TA training camps and when I made enough of a nuisance of myself they shipped me off to BAOR where they had me counting stores and painting shovels and other important items.
It is true that the alternative i.e. having to handle badly wounded soldiers and recovering bodies would have been infinitely worse but as a young soldier I wanted to see the world not paint it. So I left.
Things may well have changed since I were a lad but being bored, underpaid and under appreciated might still have something to do with the problems of retention.