it takes basically no extra effort

I’d assume one needs to verify the email by clicking a link, so to spam user1@domain.tld, user2@domain.tld would mean you need access to those inboxes. That means you need to go through the effort to actually create those emailadresses on whatever freemail service you chose, or you need to host the emailserver yourself and have all mails run into a catchall inbox.
Hosting your own emailserver is definately a lot more effort, even for a lot of tech-savvy people, paying for a hosted email service using your own domain is easier, but also seems like not a good investment just to spam a petition website.

The foo+bar@gmail.com functionality, however, is pretty well known tool - even by non-tech savvy people. Even some people I know that I consider basically tech-illiterate have known this for years have told me they found out about it and asked me if I was aware of this functionality.

The first one I mentioned preparation, setting up email accounts or an email server, the second one is basically already set up for most email users and ready to go, the latter is therefore definately a lot less effort to pull off.