No, I'm not saying software used by advisors HAS to be vetted. I'm saying that I don't know a single compliance officer that would green light a piece of software that provides any type of financial analysis, or recommendations to be used by their company as a whole without it being audited. Due to regulations, the risk is just too high. Now whether the individual advisors use it on their own is a different story. But the main issue there is that there are already an obnoxious number of channels, apps, systems that advisors have to use, the last thing most want to do is add another system into the mix, unless that system greatly simplifies things and integrates into their existing systems somehow, it probably isn't going to happen.
You're not offering advice, but you're offering the code which generates recommendations on position allocations. Any recommendation is considered 'advice' by FINRA and has to follow strict suitability requirements. Whether or not this would require any registration, licensing, etc on your part I have no idea, but it's definitely something I'd check into just to be safe. In general as long as you're not charging in some way for said advice there's no FINRA requirements, BUT that doesn't mean there wouldn't be any liability.
Every broker/dealer has their own management software/platform for client accounts, some more comprehensive than others. Though I don't know any of them that allow use by the general public, you have be be a registered rep of their firm to use them. The reason you don't see them publicly available is because of regulatory requirements regarding suitability for recommendations. Though companies like Fidelity and Schwab have some pretty in-depth tools for account management on their sites.