Cookies are broken down into two possible situations:
1. Serving of static content from a CDN on a separate hostname than the web servers. First of all, 99% of companies do not fall under the umbrella where saving the few bytes of the cookie request header is going to save you many Mbps/Gbps/packets of bandwidth. For most of us, having our example.com cookies unnecessarily sent to static.example.com isn't a big deal. Secondly, this is remedied by using a separate domain name for your CDN rather than a subdomain. Example: Facebook uses fbcdn.net rather than a subdomain on facebook.com - even though they do still use the www prefix.
2. You want separate "sections" to your website, akin to Google's mail.google.com, news.google.com, images.google.com, maps.google.com, etc. Maybe you want the cookies for your root domain to only be sent to that root domain and not all your subdomains. This is not completely ignorable, but I have personally not seen a situation where cookies on the root domain or www cannot/should not be able to be shared across subdomains.
I just find it odd that www is still considered a convention by some. If you're redirecting the root to www anyway, there is no reason to use www. You may as well use hi.example.com as your primary domain and just redirect example.com to hi.example.com. www has no intrinsic meaning, it's just a regular subdomain with DNS records like any other subdomain.
> Everything else is advice from someone who still thinks it's 1995
What about the part about cookies and static content? Why do you consider that inapplicable nowadays?