How important is it for UX designers to first take a step back to figure out what that "ideal state" is, before carrying out the incremental improvements? The former will exhaust more time & resources before outputs are produced, but the latter runs the risk of "improving a horse when we should be designing a car".
It is very important that from the start that a UX designer does not think they know the ideal state. To approach a problem thinking one already knows the solution is one of the biggest mistakes designers make. A large part of the reason UX Design exists is to tackle this issue head on.
The point of UX Design is to examine what users actually need via research and analysis. As such, in a way yes, the first thing to be done should be to take a step back and look at the challenge the users are faced with, and figure out what you need to figure out and how to get to there. Basically the primary challenge of UX is to ask the right question. Considering what the answer to this question is, only comes at a much later stage once the research is done.
Even once we get to the development stage its not a particularly good idea for a UX Designer to 'know' the ideal state and then work towards this. If you already think you know what the ideal state is then why not design that right away?
What we should know is what the ideal state will accomplish for the user, however not what it will actually look and feel like. The point of incremental improvements from a UX POV is to discover and alter the vision of what the end product will look like. To experiment with different possibilities to see which would work best for the user. It's quite a different situation to programming or graphic design, where you should have a clear image of your final product before you even start working.
TLDR: UX is about discovery. The hard part is in figuring out what the question is, not providing the answer.
One of the first things to set out when working on any project is the ultimate goal - in you example this would be the "ideal state". This would form a part of the first discovery/ideate phase of your project.
However, when working incrementally, it's easy to miss the fact that users' goals change with each iteration. If you're working in Agile (I'm assuming you are because you're talking about making incremental changes) each sprint should have it's own mini discovery phase where you look at that long term goal and see if it's still relevant as well as uncovering any issues that might be relevant to the particular increment you are focussing on for that sprint.