When I was a student, and using a shareware or trial version of some software and wanted some printed output from it without a watermark, I printed to postscript (chose a printer that supported postscript and the driver used it instead of rasterized images), but using a file instead of a printer.
I could then open up the postscript, delete the commands that rendered the watermark, save it, then I converted it to PDF so it would be easy to print.
You don't need PostScript for that. The PDF text commands are Tj and TJ, and rarely ' and ". They are easy to delete without going through PostScript. Tj means showing a simple text string. TJ means showing an array of strings possibly with space adjustments. ' means moving to the next line and showing a simple string. " means doing that and setting character spacing.
Perhaps, but it's easier to open up and edit a .ps file in a text editor than a PDF. PDF is a binary format with compressed streams, while postscript is just a stack-oriented programming language.
Tools like qpdf makes it easy to edit a .pdf file in a text editor too. I’d argue using such tools is easier than and simpler than printing to postscript.
I could then open up the postscript, delete the commands that rendered the watermark, save it, then I converted it to PDF so it would be easy to print.