What you're describing is already in place to an extent. And when examined, the limitations really stand out.
There are large budget teams that have the manpower, and they sometimes find it in their interest to race exactly as you describe. Instead of everyone trying their best, they race to maximize one athlete's best. We've seen this with BTC beating rupp at the indoor 3,000m. We've seen it in college races too, trying to get an athlete from the slow heat to run a fast enough time to score (I can remember Syracuse and VT doing this in separate races), or to rabbit their best (I think it was a pre-shuffle ACC outdoor 1500m, but forget the teams.) We've seen Geoffry Mutai win in Berlin when his teammate Kimetto backed off the pace (Mutai had a WMM championship on the line, needing a 1st place finish)
It's within the rules. But a sport where teams are mandated as part of the structure, instead of an organic emergence from the chaos of an individual sport, becomes much more limiting.
It limits the opportunities of the 2nd tier teammates. There would be many more races where the support runners are held back by trying to maximize the principal runner's race. Think about teams like the former women's BAA elite, where there was often no single leadership and the top runner could be any number of runners. Picking one to support may deny the opportunity of the team to place better with a supporting runner. We also get cases like Mutai and Kimetto, where the sport is denied a really groundbreaking performance ("How fast could he have cone!..."). You also create situations where an athlete needs a team to compete at all, and so we lose the organic nature where good but undiscovered runners have opportunities all over the calendar.
The sport would lose neutral rabbits, and lose control over rabbited/non-rabbited racing. Right now, the rabbits belong to the race director. Once teams bring in their own rabbits with their own loyalties, an individual or a principal runner with a weak team are held back by factors that don't come down to their own training, talent, or racing. Imagine some of the 2017 Berlin pacers "belonged" to Bekele or Kipsang. We now have a weaker race once they drop out and their rabbits have no interest in going further. Also, teams would show up to NYC or Boston marathons to run en force; upsets like either of Meb's wins are much rarer.
You blur national team/corporate team racing at the global championships. Do you think the 2017 10,000m would have been as incredible if it weren't Ethiopia and Kenya vs. Mo? the talent would have been distributed among more teams and their goals wouldn't have aligned the same way. You suddenly have cases where Kamwowor is also racing against his own Kenyan teammates instead of with them.
Just some things to think about before you wish organized team racing on the sport