As to the Yuja Wang clip, struggles between conductors and soloists are more common than one is lead to believe. Usually the conductor the prevails...unless, of course, you're Glenn Gould.
Conductor's role in the performance of a concerto is to provide
accompaniment to the soloist. One criticism of Brahms' 1st piano
concerto when it was premiered was that the work came
across as a symphony with the piano soloist playing a secondary role
to the orchestra. That might explain why the concerto never gained
much popularity in the 19th century when virtuoisity of the soloist
was often the selling point of a concert.
I don't think the soloist has to be a big name to dominate a performance
or at least to be a equal partner to the orchestra. Obstinate conductors who
always tried to dominate the soloist in the performance of a concerto is
a rarity. I can only think of Toscanini, Karajan and perhaps Georg Solti as the
few prominent conductors who rarely demonstrated the kind of sensitivity
and restraint required of a good accompanist.