I think there are two separate meanings to a “discipline.”
In one sense, it is a way of thinking. To a learner, it is desirable that everyone be at least reasonably familiar with how people in different disciplines think. Mind you that I began as either a historian interested in physics (I soon found out that I was really interested in math instead, especially probability theory), or a physicist interested in history, and having both backgrounds, and a few others along the way, was immeasurably helpful in helping shape my thinking.
In the other sense, however, a discipline is a body of technical knowledge pertaining to a given subject area. You can’t be a physicist without having gone through the set of commonly agreed upon coursework and having achieved a degree of specialization thereof, not just because you can think like a physicist. The technical definition of the discipline can’t be dismissed easily, because techniques and formulas do take a lot of time to learn properly.
One thing that always bugged me about teaching statistics was that we wind up losing so much time going through the introductory stuff on the “formulaic statistics” that we don’t get enough time to teach how to think like a statistician. Unfortunately, you have 10 or 15 weeks to teach undergrads in social sciences something about statistics, you have to make choices — and sometimes, you don’t really get much discretion, even though it would have been far more useful that they should have been taught the latter rather than the former, in my opinion. This was reinforced much more when I started running into data science people in the industry, whose idea of “statistics” was grounded on the kind of formulaic statistics that I thought was misguided, and would have found it far more enlightening had they been exposed to more of the foundations of statistics that are not (necessarily) formulaic. So this is an example where the notion of discipline, defined as a specialized body of techniques, combined with constrained time available, was forcing a way of thinking as if it is the gospel truth and not doing even that very effectively.
But by the time students get to college, it might be too late to get them to think creatively and vertically, given the time available. The foundations need to be laid much earlier so that the material being covered can be processed much more naturally.