Well, no you don't want to be the EOC. And, you should feel free to roll on the floor laughing at anyone who does. The stated desire to become the EOC means "we do not know enough about the kinds of people we want to attract."

The truth is that you know a fairly large number of people who you hope will go to work for your closest competitor. You may even have people on your payroll who would make life better for everyone if someone else were their personal EOC. There are plenty of really wonderful people who you pray will not waste your time by trying to find a place in your company.

Ambiguous goals result in performance failure.

Unfortunately, when we all learned to avoid labeling and stereotyping by using the phrase "people of color" (that was a good thing), we appear to have given the HR jargon factory the authority to mint new, linguistically twisted and meaningless phrases like EOC. These are the same people who use language like "I have issues around that" when they mean "I'm concerned about that."

If you are a software company, you don't want to be the employer of choice for bricklayers. If you are a local establishment, you don't want national status. If you are a hospital, you have no need to be interesting to R&D Engineers. 

On the other hand, you may wish to be the most desired place to work for certain subsets of the population. That's where the questions of branding, communication, traffic development and candidate pool development become critical in employment design and your 'employment brand'. The notion that HR is responsible for managing 'desire' outside of the company's walls is sure to raise concern in the head-shed and the marketing department.

Every company is capable of changing some of its dynamics in order to become desired by a targeted demographic subset. Being more than you need to be is an unjustifiable expense, so, precision is the watchword. The real question is "who are your dream employees and what do you want them to dream about?"