I assume that search engine robots crawl the whole page and then the canonical tag because pages that are self canonicalized still get indexed and their contents are still parsed.However, does a self canonical link cause an infinite loop wasting crawl budget?
Does a link rel canonical tag pointing back to the page itself cause an infinite loop that wastes crawl budget?
web crawlers;rel canonical
Bots dont blindly follow all links on a page. A bot remembers the URLs it has crawled and the URL it is currently crawling. If it finds a link to one of those URLs again (something which happens all the time -- think of the site navigation, for example), theres typically no need to crawl it again for some time. Well, technically they could, of course. And there are likely some peculiar/bugged bots out there that do this. But it would not only waste your resources, also the bots. So bot providers have a reason to make their bots smart: saving costs.