tl;dr start small, prove the concept, and then build up
I'm going to start by thinking through what a manager might respond if given the proposal (based on the information you've given), and then what you could do about it.
Is the cost-benefit worth it? There are probably hidden costs
In reading the response of your supervisor, you've focused on monetary cost. But there are probably additional costs you haven't factored in. What you're asking from your supervisor is actually a huge deal, and could take years to agree and implement, even if everyone wanted it.
I work in naval architecture
Is your role as a software engineer, responsible for creating new programs to decrease human labour? If you have another role, any time you spend on this is taking away from your normal responsibilities. Any time your supervisor (and his supervisor, and legal, and accounting, etc.) spends thinking about and approving this is taking away from their normal responsibilities. So even seriously considering this idea might cost your company hours of working time.
we don't know if it will work
Your supervisor is wise here. Even if your product is well tested, there's no guarantee it will cope with everything "in the wild". A made up example, but you've tested it produces an error if the price is greater than the company's limit of $100, but the CEO has given approval for some $200 products you didn't know about.
How do you find and fix these? Do you role it out gradually, checking the first few uses in great detail (which takes time away from other activities?) Do you role it out to everyone, and just accept there will be bugs? In naval architecture, could these bugs mean loss of life, or destruction of multi-million dollar equipment? Are there legal certifications you need to get before this software can be used?
I was very clear that I already did the necessary work on my own time, and it will not cost anything. Other than pasting the code and running it.
Who owns this code? Any answer to this could put your company in tricky legal waters (although I am not a lawyer!). If you own the code (since it was done on your time), then the company may need to write a contract and "buy" it from you. You could open-source your code, but that brings its own complexities. If the company owns the code, then any time you spent writing it could count as overtime. Local laws or company policy may require this time be paid, or you may have broken some maximum overtime limit.
It can circumvent a lot of manual labor and reduce human error
How many hours of labor will it save per month? How many people does this mean your company can fire, and how does the wages saved versus severance paid work out? Alternatively, does this free employees to do something else, and how much money does that save/create? Might your company be breaking local laws, or union agreements, but suddenly changing these workers hours or responsiblities?
In terms of human error, how often do these mistakes happen, and how much does each cost? Will it save the company from a million-dollar law suit once every ten years? Does it stop over-orders of stock by 10% each month? It might be that you've perfectly solved a problem, but it isn't actually a problem anyone cares about. (For example, companies dumping waste into the ocean, because paying the fine is still cheaper than cleaning it properly).
So in a way, I feel like I'm being denied an opportunity to grow.
If you're current job isn't in AI (or software), then you're boss doesn't have a responsibility to help you grow (in AI). He only has a responsibility to help you grow at whatever it is you're employed to do.
How can I better approach my supervisor? You start small
As you can see, there are lots of questions that need to be answered before this becomes viable. You can try to answer them by writing a longer proposal, but ultimately "the proof of the pudding is in the eating".
So, my advice would be to start small. Is there a way you can use this technology to solve a problem just in your job, or your team? Is there a small daily frustration for your supervisor that you could remove? You might find something like "Can I try this on my own machine?" is more likely to get an answer "I don't mind, as long as your reports are still accurate and on time". Once you get it working for you, you can talk to your coworkers about them trying it. Gradually, you'll build up the process and begin to answer some of this questions. Once the software has "proven itself", you might find your manager is more willing to invest in it.