I have a similar setup, but I've automated a few more steps.

I have couchpotato[1] running on my VPS. When I add a movie to it, it'll find and drop the torrent file to a directory, where rtorrent will pick it up and immediately start downloading it. When it finishes, it moves the files to a temporary directory, where couchpotato will detect them, rename them and move them to yet another directory, where Git Annex Assistant[2] will add them to its store and sync to a Raspberry Pi in my home through SSH/rsync.

Then I can either copy the file to my laptop or Android by doing "git annex get <file>" or stream it from the Samba server running on the Pi.

Complicated to setup initially, yes, but now it runs smoothly with almost no manual work.

[1] https://couchpota.to/

[2] https://git-annex.branchable.com/assistant/

What is the advantage of this compared to just running everything on the pi?

Well, I like to keep decent ratios (usually 3), which would keep my asymmetric home connection too busy - whereas my cheap VPS can do 1Gpbs (burst). And in my experience, the Pi doesn't handle well heavy random IO over the USB/ethernet bus - I had downloads with 20-40% of blocks corrupted upon verification.

And of course, while I don't consider it a problem where I live, removing the torrenting from your connection to a VPS in the Netherlands reduces the chances of having legal problems.

And the VPS isn't a dedicated seedbox - I'd still use it for my email server (Spamhaus' PBL prevents me from sending from my home connection), Tiny Tiny RSS hosting, website hosting, etc.

Put.io "Seedbox As A Service" should work pretty well for that purpose

That's what a seed box is for. If you're really paranoid about it, you can actually pay for a seed box in bitcoins. Cost a good ~$20 a month though.