My experience is dated by almost 40 years, but, again reversing the roles, it seemed we groundpounders used to do a lot of work that was supposed to be done by the combat engineers.
Chill out.
Yup you're right, never enough Engineers to go around.
Individual and small unit field fortifications are properly constructed by the using unit. The larger mission of expediting the forward movement of the supported unit is the Combat Engineer mission.
NEW ITEM: See new post, dated 7:11 PM PDT, that one BDE of the 2d Infantry now in Korea is headed for Iraq!