There probably is an avenue to automate printing from your desktop as soon as it receives the email; who knows, maybe even
The inconvenient of your way is that your bookmarks are only available on the Desktop, from your mobile all you can have is the list of URLs you sent yourself. It's still probably better than having some service running all the time you want to query though.
Your system is surprisingly "low-tech" and sounds extremely interesting, I'm tempted to start doing it as well. Do you have any kind of organization or viewer for your stack of PDFs, or are they just files amassed on your hard drive ?
And as for the mobile/desktop issue: I just sync my PDF dir to my mobile phone, and carry it all with me, anyway. The mobile version is not as grep'able, but its pretty neat to have every interesting website I've ever cared enough about to print-to-PDF with me in my pocket, even if it is a nearly un-navigable list of 20,000+ files to scroll through, hehe ..
Go Share...-> Chrome (Print) --> (Brings up "Save to PDF" (!!)) --> Save to Drive (and then sync this drive to your computer).
You could also save to Dropbox or whatever other syncing service you choose.
Still, would be nice if the Browser vendors would cotton on to how powerful this is, and make the whole thing a bit more seamless for the mobile/desktop bridge, or just make Print-to-PDF work more smoothly for this case on mobile.
Either way, I also have a list of every mail I've ever sent myself containing a URL from mobile, which is handy in and of itself at times, hehe ..