I’ve never run a company, but I’ve worked on and shipped games since before the iPod existed.
You seem to be discounting the factors that would make this a realistic plan. How much experience do you have developing games? How much experience do you have running a business? Since you call it “game design industry”* I’m going to guess your experience in the industry is on the low side, and that is a big concern.
A few years ago, I worked for a rather large game company as it peaked and disintegrated. Lots of smart people with tons of experience went to form their own studios. Most, if not all, needed external funding to compete. Some of them even had successful game launches, profitable and popular.
Not one is still in business. It takes a lot more than making a profitable game to succeed.
You have to ask yourself if you really “prefer” to deal with personnel management, accounting, legal, QA, customer support, maintenance, hardware and software purchases and all that running a game studio entails? Or do you just like the idea of being a video game creator, with accolades from fans and a passive income from sales? That last one hard to come by**, but the rest are required to start a game company. Even if the only employee is you, and you already own all the hardware and software you need, you still will have to do all the paperwork that makes your company a company (which barely scratches the surface of reaching the point of releasing a commercially viable game).
You might be thinking “[indie-example] made it, surely it’s not that hard!”
It is that hard, and probably harder than you imagine.
We remember they made it precisely because it’s unusual. On top of that, they were helped by the timing (new platforms, new audiences, new investment, new technology).
Preferences are a nice indicator, but if you want to get started in the game industry, then start with a job in the game industry. Nothing beats full-time development like working with someone who is going to pay you for it. You’ll get experience that you’ll need to run your own studio, and maybe learn that your own studio is not actually what you want. With more and more experience, along with a demonstration of skill (and luck), you’ll be able to work at the types of places you want to work, and select, if not spearhead, the types of projects you want to work on.
As an engineer AND someone with the skills to create highly-detailed 3D models, you are correct in that you wouldn’t have a problem getting a job. Technical artists are often in high demand. With such multiple talents, you’d have a good shot at hooking up with a smaller studio, or even a start-up. Working at a small place puts you closer to seeing how it all comes together, and gives you a much better chance to make a name for yourself. Advice from every investor usually includes something about getting started with someone else’s money. Only a fool stakes his life savings on a single all-or-nothing shot.
Once you have a job in the industry, you still won’t have enough time to work on what you want to work on (in all likelihood, you’ll have less - game industry hours are some of the hardest, plus you’ll be spending creative juices at your day job). Still, you’ll be getting the experience all the same, and you can be saving up for your next step.
Which leads to another suggestion. If all you want is the pride and satisfaction of making your own game from the ground up, without working for (or with?) anyone else, then save up the money to buy yourself the time. How much time off do you need? You’re probably going to underestimate, but you’ll also be surprised how much you save not working (a lot of it is driven by a much more frugal mind). Be sure to include a cushion for any project investments you might need (such as testing or special art).
But absolutely do not jump from stability into the deep end. Make sure you know how to swim. Or, if the plan is to learn swimming the hard way, at least bring enough supplies to allow that to happen.
*Game design is just one job. Albeit probably the most important, I’ve never heard anyone use “design” to describe the industry. If you do go with applying for jobs in the industry, don’t refer to “game design” as anything other than a type of job or a critical process. “Game development” for the work and “game industry” for the industry are good catch-all terms.
**Actually, it’s a bit easier if you’re not concerned about time and money. I know at least a dozen of people who have been working on a game, or releasing a bunch of tiny games, for years, sometimes decades, with hundreds, maybe thousands, of fans. It’s all spare time and no-profit work, but they have work they are proud of with a community that is able to keep the excitement going. By any commercial game standard, most of their games look pretty awful, and/or involve mechanics that are user-unfriendly at best. But they’re happy with the work, and their fans seem to love it as much as any big title or sports franchise. If this seems good enough for you – perhaps you have one game you want to make without interference or a bunch of small ones without overhead – I highly recommend it.