I have a fundamental question about Quantum Mechanics or even mechanics in general. I am aware that there are stationary solutions and non-stationary solutions. The stationary solutions solve Schrödinger equation for time independent Hamiltonians, whereas non-stationary solutions are used to solve for time-dependent Hamiltonians. However, my question is whether strictly speaking there shouldn't be any time dependent Hamiltonians at all. The whole approach of time-dependent Hamiltonians seems artificial and premeditated to me, because one has to assume dynamics or evolution at a certain layer, which should actually be a prediction of the theory.
Based on your comment it seems like the issue is that we should make our system large enough so that our system is closed. While there is nothing wrong with this, you might be making the problem way harder than it needs to be.
For example, if we are looking at a particle in a time varying magnetic field, if we are only interested in the behavior of that specific particle then we would not want to describe everything else that is causing this magnetic field. We could include everything, but it does not help us to do so.
So if you definition of contrived is that we are not including the behavior of everything that makes the changing magnetic field, then you can call it contrived. However, in most situations this is a lot better than keeping track of many more things.