I went through the same process this past year: my job had gotten to the point that the most challenging part was trying to accept the level of dysfunction that had become so entrenched. I was in my chosen field, getting to work on the exact thing I wanted to work on. However I could not shake the feeling that the organization could give two shits about my actual performance, and really just wanted a seat-warming sycophant. I had been in this position for almost three years, and all the economics (profit sharing, benefits, etc. ) were favorable.
Leaving a "good" job is not easy, even when you have another "good" job lined up.
Luckily my wife gave me an out in the form of becoming the stay at home dad for some time while she became the breadwinner. It's a tighter budget, but doable. It also aligns with our desire to avoid having to resort to daycare for our very young children.
I did not really want to leave just as I was moving onto the work I really wanted but the nagging feeling was still there: do I really want to hitch my cart to this drunk pony?
My solution was to do the things I was specifically directed, but to get those out of the way as fast as possible, as opposed to the usual milking it out and "looking busy" until the next task came by (this was common between large projects). With the rest of my time I dug deep into the things I believed were the most critical to the company, were related directly to my position, and were also problems I could solve. Without getting into too much detail, I sought to improve some of the processes that were either outdated, outright wrong or maddeningly cumbersome/tedious.
I did this for about six months in a few different areas I was involved: systems modeling, database management, and radiant heat transfer were the three that I focused. I wrote some simple proposals, some mock-ups of what I was building and presented it to my superiors.
The response was utterly unsurprising given the the track record of the company: "we have always done things this way", "it has always worked fine so far", " we need that cumbersome software because someday, it might prevent an expensive mistake", "I make the decisions and am responsible so you just need to accept these practices and move on" etc. I pointedly asked my boss (the chief engineer) if he had any questions, anything, about one of my proposals (maybe 25 pages long) and the answer was a flat "no".
That was the last straw. If my best work was going to be so curtly dismissed, I would rather change diapers all day.
Granted, I was being one of those "if I was in charge this is how I would do it" types, but I was A: putting it in detailed written form, and B: confining my proposals only to what applied directly to my job. It wasn't water cooler bitching, and it wasn't about telling anyone else how they should do their job.
Don't cope with an unsatisfying job any longer than you have to. My advice: decide for yourself what you can do for your company, and then do it (enlist your fellow drones of you can). If your boss/employer (go as high as you feel comfortable) does not at the very least recognize your work ethic, tell them to shove it.
TL;DR It feels great to leave a sinking ship after you tried, and were told not, to fix the hole.