> RIPE Atlas is primarily designed for INTERnet measurements, not Intranet.

Emphasize on the "primarily", that doesn't directly mean private measurements shouldn't exist. 

> If one has a problem with open-data philosophy, he shouldn't participate in this project.

The existence of a token system already incentivizes contributing, without just making good public measurements that contribute back open data.

> It shouldn't be necessary to run the same measurement multiple times. For what reason?

Because things change in the wild?

> There's only one exception

Well... So in addition to lack of a good basis in principle, non-private measurements might also pose an unnecessary additional information leakage. In addition to that, many measurements are just absolutely useless for others.

I am also certain there are people who only contribute (by hosting a probe) for that reason - running a few private measurements.