Stretching the sense of the range of possibilities within rules, even when they are somewhat arbitrarily self-imposed, prepares us for finding connections that might otherwise be missed. Professionals complain that time demands don't permit the luxury of creative experimentation. One reason for being as exhaustive as possible in school is to build a facility for seeing the potential in new projects without investigating all the possibilities concretely. Another issue is that many ostensibly time-constrained projects end up being rather drawn out and could have allowed for greater freedom in early stages. The second part of the question raises the issue of leadership.
Vocational training is meant to serve the status quo industry.
An intensive but broad-based education can and should contribute real innovation and consequently lead. The distinction seems unavoidable in our present day situation, but the crossovers are probably just as characteristic. Each draws from the other, stimulates the other. Ultimately, design can be self-expression only as it is relevant to an externally defined problem in an interdisciplinary and collaborative environment. And yet you also suggested that, as designers, we are always in the process of seeking those gaps.