I haven't tried this app, primarily because I have collected most of my serial numbers manually. So I don't need Mac Product Key Finder Pro. That said, I think it's easy for people to have elevated expectations for what an app like this can do. Before paying for the Pro version, or even the free version, you should visit the developer's web site and review the list of supported apps (https://mac-product-key-finder.com/supported.html).
If Mac Product Key Finder Pro cannot find the serial number for any of the listed apps that you have installed, then you have something to complain about. If you have an issue, I suggest you communicate with the developer privately so that he will have a chance to figure out what's not working. That's not to say you shouldn't post here as well, but if you actually want a solution to your problem, working with the developer is the only route to take.
Personally I can only imagine the work involved in figuring out how to find serial numbers for all the apps listed. One would have to have made a serious study of the subject even before building an app to utilize what you learned. Perhaps, though, he could have used more beta testers to root out problems. It might have saved him some of the flack he's getting here it the app had been more thoroughly tested.
Still, if he can improve the software so that it's more reliable, and make a bigger point in the promo blurb at the top of this page of directing potential customers to the supported products page, it may eventually be an important tool for people with large investments in software. Programs can themselves lose track of their registration information when something dramatic happens to the system on which it's installed. An operating system upgrade can cause this, as can restoring your system from a Time Machine backup. I've seen this happen with Adobe apps in particular in both these situations.
So having your serial numbers handy can be important.
By the way, since most software is now purchased online, your serial numbers will be in the e-mail receipts—if you saved them. That's how I found most of the serial numbers I've catalogued. I've also made a habit of printing to PDF the web receipts I get after I buy something. If you didn't save your receipts, well...you need Mac Product Key Finder Pro. Even though I haven't used this product, I'm going to give the developer an A for effort, just to balance things out a bit.