Until recently, that was a contradictory set of goals. Now it's pretty feasible to achieve both goals using C++. But, not so much with hand-written JS... (Feasible, not arguing theoretical)
Kindasorta. They do contradict if you only write one program. But you could write a high-performance 3D game and a web app and achieve both goals, thus justifying learning both JavaScript and C++.
What makes you think that many web developers don't already know C/C++?
Many developers choose the web because there is their audience, their business, their future.
And we know that people don't like to install stuffs, they want to consume a product LIVE.
I don't mean to write your app in it, I mean using it for optimising tight loops and such, just as C developers occasionally write some functions in asm for performance.