I am one of those who holds a flying licence as well as an engineering licence, but like most of my bretheren, I am an engineer who became a pilot (and probably not particularly good at either although it doesn't stop me trying harder).
Personally, I am not aware of anyone who started out as pilots and then became engineers as well. There are a number of reasons I have been presented with by the piloting fraternity over the years as to why they do not have any interest in becoming engineers.
For some, the idea of getting dirty doesn't appeal.
For others, the thoughts of ridiculusly long hours doesn't appeal.
For others, the thought of the years of training at poor pay rates just to gain a basic engineering licence doesn't appeal.
For others, the thought of working your heart out trying to get the job done as quickly and safely as possible to the highest possible technical standards, only to have some spineless managerial type complain that engineering is a drain to profits, doesn't appeal.
For some, the level and weight of responsibility which generally far exceeds that of a pilot, doesn't appeal.
For some, the massively increasing burden of paperwork and legislation doesn't appeal.
There are other reasons often stated, though they tend to be less mature.
But, if you are still interested in the idea, go for it.
camlobe