Engineering is not a single major; the various kinds of engineering do not generally have interchangeable faculty and subject-specific facilities and equipment. Note that even the more usual types of engineering, like civil, chemical, electrical, mechanical, and computer, can have ups and downs in demand, usually following industry ups and downs.
However, it is true that many engineering majors at many state flagship level universities are oversubscribed most of the time, so expansion would be desirable as a longer term project. But there are probably funding and internal political problems that get in the way.
Universities are probably cautious about expanding new or existing departments or programs, since hiring a tenure track faculty member is a multi-year commitment (much longer if s/he gets tenure). Yes, they can be more “nimble” by using adjuncts more, but would that really be desirable for the upper level courses that are likely the reason for capacity limitations? But such caution about expanding departments or programs means that oversubscribed majors can be a persistent problem.