Brave New World proves once again Team Cap was the only choice

SPOILERS FOR BRAVE NEW WORLD

Putting the Avengers in the hands of the World Security Council, and by extension Secretary (at the time) Ross would have been disastrous.
Knowing what we know now about Ross and The Leader, Ross becoming Secretary in the first place was probably orchestrated by the both of them.

This would have put the power of The Avengers in hands who are now proven to have been the wrong ones, and things only would have gotten worse had Ross become president with the whole team complying with the Accords.

Like Steve Rogers himself said, "The safest hands are still our own".