This is true but to use your example of an emergency room:

It's not uncommon in more rural areas to find a business that is essentially "more than an urgent care but less than an emergency room". e.g. they aren't doing trauma surgery but they can deal with broken limbs, severe lacerations etc that an urgent care couldn't handle.

My point is that while it's true that there are "step functions" in certain services, this is not always the case.