Your job and experience sound very similar to my current role. I don't have an accurate job title anymore, and I very much see myself as the oil that makes the engine of the company run more smoothly. I wear about four or five different hats, all depending on what fires I need to put out. Good to meet someone doing something similar.
A firm without This Guy means that more small problems/needs get ignored since it doesn't clearly fall into anyone's scope of work or warrant the cost associated with the specialist. And if it gets large enough to not ignore, a specialist will consistently have to context shift to something outside of their specialty when something tangentially related pops up. This decreases their productivity considerably, decreases their satisfaction as they can't focus on what they truly enjoy doing, and increases business risk as things get overcomplicated or slip through due to a more biased view on the strategy to perform the work (based on whatever the individuals specialty is).
Practice-wise, it astounds me how many people/institutions expect different results from everyone else while hewing to the same practices as everyone else. Why do you think you'll be the exception? Why can't you look at the reality of what is working and what isn't?
This applies to so many areas of life, but it is extremely pronounced in business, where everyone cargo cults every little practice of AmaGooFaceSoft and believes that is what made them who they are. It's like there's an extreme deficit of original thought.
It's incredibly hard to get a job. But your versatility will ensure job security for as long as you care once you're in the door, thanks to your ability to get into the critical path of different department's operations.
I'm a competent, high performing generalist who can work autonomously and self-sufficiently with enough confidence in my capabilities to have a high risk tolerance. In my current company I got tossed around from starting under a marketing manager, to getting shifted under the CTO after stepping on IT's toes too often, to getting pushed into a newly formed Operations group, to finally just reporting directly to the owner. While officially I manage a data management and BI team, in practice I'm the guy you escalate random problems and needs to. Creating a BI team was a byproduct of being a generalist and being the first person that needed a consolidated view of everything (and having the ability to execute on that need).
Looking for a new job is a pain. Companies don't explicitly hire for it, politics can come into play if the generalist doesn't know how to dance around the company in a way that doesn't threaten others' fiefdoms, there's no easy way to suss out competence from arrogance during an interview, no manager wants to frontload your salary on their budget when they won't be getting the full benefit of it, and a host of other things.
Generalists are valuable to a company, holistically. They're oil to the machine and fit in between all the specialized cogs to smooth things out and let you run the engine hotter without breaking down. But managers only manage their own cogs, hiring only looks for the cogs they're told to find, and at the end of the day whether there's oil in the machine is Someone Else's Problem. Very few teams exist which have the prerogative and budget to hire for that holistic need, so most companies just go without oil and don't think about it ¯\_(ツ)_/¯.