I think the author of this tool is totally missing the point of the print/sign/scan legal hoop that one sometimes has to jump through. The law sometimes requires certain documents to be "in writing" and there is, unfortunately, a legal tradition tied to this that "in writing" means "physically on paper", which many lawmakers and bureaucrats unfortunately haven't managed to properly transition into the digital age.
However something that is quite a separate matter is the question of whether one needs to actually be in possession of that piece of paper. A scan of an original serves as proof that the original exists. ...and this is usually all that anyone requires for practical intents and purposes.
But: You're not supposed to do print/sign/scan, and then just throw away the original. You're kind of supposed to keep it in case you're ever asked by a court to produce it. The document partially loses its forensic value if no original can be produced.
If that's the point, why does nobody ever say to keep the original?
If the counterparty needs it, why don't they request you sign two copies and send them one? The idea that they would later want it for forensic evidence that you really did sign it seems odd: if it's in their benefit and you wanted it to not exist, and you're the one possessing that original copy... you can make it not exist.
I guess, when such administrative procedures are decided, then the kinds of considerations that go into it have to do with whether the document is more to your advantage or more to theirs. In a high stakes situation where the document is to their advantage (like you sign an employment agreement), they routinely will insist on having a signed original rather than just a copy or scan. In situations where the costs of dealing with paper originals outweigh the potential benefits, they might well not insist on having paper originals.
But, to come at it from the other side: If you want to make sure you can actually rely on the document in court, it's probably a good idea to keep originals and definitely a bad idea to use this FalsiScan tool.
The lowly-paid administrator who deals with you might not be able to detect the FalsiScan that you submit. But if something goes to court and it benefits them to undermine the forensic value of the document, then you might well find yourself faced with a digital forensics expert proving to the court that the document came from this FalsiScan tool. This opens the possibility that, for example, a third party with access to your computer that contains all the digital assets to create FalsiScans (like a scan of your signature) could have created the PDF.
It's not obvious that you would want to respond to that by saying "but I definitely definitely did use FalsiScan myself, meaning the PDF to represent my signature on the document".
If the other party can make it look like you purposefully sent something that would make it past their administrative procedures but would have questionable forensic value so that you could later have it thrown out in court, then you can no longer rely on the document yourself and could even be liable to damages that resulted from their relying on it.
If they can clear a slightly higher burden of proof in the general direction of fraud, they could even come after you criminally: Fraudulent creation of digital assets of forensic value (like scans of paper documents) is a criminal offence. -- At least in Germany; I don't know U.S. law that well.
That also applies to your original suggestion about making a document not exist whenever it serves your purpose for the document to not exist. ...that too is kind of a criminally relevant thing that you probably don't want to do.
However something that is quite a separate matter is the question of whether one needs to actually be in possession of that piece of paper. A scan of an original serves as proof that the original exists. ...and this is usually all that anyone requires for practical intents and purposes.
But: You're not supposed to do print/sign/scan, and then just throw away the original. You're kind of supposed to keep it in case you're ever asked by a court to produce it. The document partially loses its forensic value if no original can be produced.