When you go to a website, say Bevelwise for instance, do you type www.bevelwise.com or bevelwise.com in the address bar? If you care at all about SEO what your users type into their address bar should concern you.
Personally, I type the www because technically bevelwise.com is the main domain, the house that all of the services live under. By typing the www I am telling bevelwise.com that I would like to see the website of bevelwise.com. If I were to be transferring a file I would be using the File Transfer Protocol, and I would expect the bevelwise.com house to be looking for this type of access request at ftp.bevelwise.com.
I understand that www, ftp, cdn, rss, etc, are all just sub-domains on the main domain of bevelwise.com and that what really matters is what protocol / port is being used to make the request.
To take this to a more relatable direction, let's take a street address: 1313 Mockingbird Ln. We can analyze this address in much the same way as we do a domain. Consider if we think of the domain "bevelwise.com" being the equivalent of the street "Mockingbird Ln." Now, if we wanted to go to the Munsters house (1313 Mockingbird Ln. is their address on the TV show), we could technically find the house by going to Mockingbird Ln and looking around. I assure you we would eventually find it and get what we came looking for. But, if we add the house number (1313) to that address, we have the complete street address of what we are looking for, much the same as when we put the www in front of a domain when we want to go to a website.
I know there are a lot of people out there in the technology industry that are of the belief that the www is irrelevant and unneeded and is only added as a DNS record to help those people out there who don't know any better. However true this may be from a purely technical standpoint, we need to think about the users of the internet who, as a majority, are not technically savvy.
So, from my understanding, Google will see www.bevelwise.com and bevelwise.com as two different and separate sites regardless of the fact that one is a sub-domain and one is a primary domain. It will be seen as 2 sites with the same content and will get a negative mark.
Now to help with this issue, we basically have 2 choices in this scenario. Forcibly add the www via 301 redirect when someone goes to bevelwise.com, or forcibly remove the www when someone goes to www.bevelwise.com. I personally lean towards adding the www in any case where the address requested is not already a sub-domain request (i.e. bevelwise.com will be changed to www.bevelwise.com, but ftp.bevelwise.com will not be changed to www.ftp.bevelwise.com because ftp.bevelwise.com is already qualified with the ftp prefix).
Just for fun, take a look at your browsers address bar right now, when coming to this site, did you put the www in there or no, any reason why you did one way or another? Call it a personal and professional curiosity.