I'm wondering: suppose I have a website for chicken restaurant and my domain is
chicken.com, shouldn't be better to have main site on
restaurant.chicken.com as primary domain (root domain) in terms of SEO and PageRank?
I would not recommend putting your main site on a keyword subdomain and redirecting
www and the bare domain to it. I have a friend that does this with this website and he regrets it.
He doesn't see any SEO benefit to having the keyword in each of his URLs. Google doesn't seem to be giving much weight to any keywords in URLs right now. It just doesn't seem to be a strong ranking signal right now. You might want to create a handful of pages that use that keyword in the URL path, but having the keyword in every URL for the site isn't needed.
Users expect sites to be on a naked domain, or
www. Having a different main subdomain makes your URLs longer, harder to remember, and harder to type. Usability is now a stronger SEO signal than URL keywords. Anything that hurts usability shouldn't be done in the name of SEO.