What if "promotion" doesn't necessarily mean domain over other people, which seems to be the other issue. There can only be one SVP of Technology, for example, in most organizations.
What if, like in school, you get "degrees" for achieving things within the organization? If you launch a major new product successfully, you achieve a "master programmer" honor, and the associated pay benefits. This doesn't necessarily give you any right to control others in the organization, but it rewards employees for stellar performance. They can then put that on their resume if they go to another company.
I would argue it is a little short-sighted to say that the company can exist in a vacuum, when every other company in the world, for the most part, operates with a title. That doesn't mean you have to play that game within the company, but you should at least accommodate employees' concerns that they work for you for 10 years, and then can never get a comparable job because it looks like they never advanced. If they stay in your good graces, it probably isn't an issue, since I'm sure you will give them a good recommendation. But if not, they could be in big trouble when they go to find a new job.
A large part of management structure in the first place is to try to insulate the organization against changes at any level. Want to replace the entire C suite and the board? No problem... business goes on as usual. With this structure, the company becomes highly dependent on the people at the very top. Any changes there might have the effect of blowing up the whole organization, because there are only a few people who are unquestionably in charge. I think there are lots of benefits from trying to reshape the corporate org chart, as I mentioned in another post, but it is also dangerous to be overly idealistic in terms of how your employees regard this structure and the risk they place on working under it. If most of them feel its appropriate, then I suppose there is no problem. However, I wouldn't automatically assume that's the case, just because they have chosen to work without a title. Also, a large part of their continued work at the firm may have to do with their relationship with you personally, which may put the long term viability of the business at risk.
Why should anyone optimize for the irrational job-hirers out there? This does not sound like a path to happiness to me. Besides I find it unlikely that the kind of person who is happy at a small company like 37s for 10 years would want to work at this hypothetical irrational company.