The culture centers on completion because that's so damn hard. The fastest riders, however, are absolutely racing each other.
Would you say that Tour Divide or TransEurope are not races, because enough people fail to finish them that the focus is on completion, not competition?
Another reason why the culture is different: drafting is not widely used, and pack formation is rare. This magnifies the effects of very small differences in riding speed so that riders are generally widely spread out. I know from own experience doing brevets in the 90s that it would be rare to be in visual contact with other riders. Same is true for Tour Divide, TransEurope, RAAM etc. This makes "competition" look and feel very different than in pro-cycling and cat racing where "can I hang with the pack?" and "should i attack now?" are the constant questions.
However, all the same things are true of ultramarathon running too. Limited visual contact with other racers, high DNF rates, completion being the goal for the majority of participants. Nobody says, however, that WS100 or UTMB are "not races". And the reason for that is: in this category of racing, there is no other format. Nobody runs 100 miles like the pack on a track and field event, or even the way most major marathons play out. The nature of racing WS100 or UTMB just simply is the nature of ultramarathon running races.
And so it is for cycling. When you increase the distances and terms (e.g. "the clock runs non-stop"), the nature of the event changes. PBP is nothing like any TdF stage, but it is still a race. Granted, more like triathlon where only a small percentage of the entrants are actively racing other people, but people don't say that's not a race, either.
I think a thing fit all the definitions of something while not being that thing. For example, tomatoes are berries according to the definition set by botanists, yet if you ask anyone in genpop they consider tomatoes a vegetable because that is how people view them.
I’m not trying to disagree that PBP isn’t a race, because i acknowledge it fits the definition of a race, but I hope we can agree that calling it a race does a disservice to its history and culture.
For similar reasons I wouldn’t consider the Tour Divide a race either because the organizers don’t call it a race. For the same reasons an ultramarathon or rides like Unbound, Silk Road, TransAm, or Transcontinental is a race; because the organizers call it one. Is this a rational viewpoint? Definitely not, but that’s fine with me.
There is a power in what things are called and I think it is important to stay true to roots.