I think, for this to be useful to more than a small subset of startups, each stage needs to be far more broad/vague, more focused on the product(s), and less focused on the company composition. (It was especially jarring to base maturity on team composition/interaction, since not all startups/businesses have disparate teams.)
For example, my 4-year-old biz is probably somewhere between "Problem" and "Platform" since I still routinely change the product(s), focus on building around new areas, and groom the core skeleton.
But, of course, it's also had times where "Process" and "Pace" where the focus, and times where I've focused on other projects for months at a time where I'd say it was all the way in the "Profit" stage.
As you say, all these focus areas exist at all times and you can only prioritize on one (for the most part), but I wouldn't call these sequential stages that you go through in order while a business grows -- rather, just 5 different pieces of the "running a successful business" pie.
