It's not quite what you want, but you can improve the output by selecting 'reader view' in your browser first. I use Firefox and this is just a button in the URL bar - I know Chrome has a similar feature but I can't see it (found the setting that says it's enabled!).
Firefox
Basically it shows the content of a web page without headers, etc so when you do a print to pdf now you get less clutter ...
@casportpony - I hope you don't mind me using your article as an example, it's just so that it's easy to compare the output
Attachments
Treating Coccidiosis with Corid, Amprol, AmproMed.pdf
Edge Chromium has an immersive view feature but it doesn't look as though it works on this site? I tried it on a BBC news article and got the following button ...
I'm guessing this is browser dependent rather than the web site as I've tried a handful of other random articles and it works on everyone in Firefox.