What does Silence do?

Four seconds is the whole window, so silence pays off only if you act inside it. An enemy that cannot use skills is left without the moves that make it dangerous, which makes silence the moment to commit your own damage rather than play safe.

Your own active skills cost Energy Points, and that EP comes from one pool shared by the whole party. Spending a burst of skills into a silenced enemy is a good use of that pool. Spending it after the four seconds have run out is less so, because the enemy is back to full use of its kit while your party's energy is lower.

Silence is not the same as Break. Depleting an enemy's break bar stuns it until the bar refills and makes it take greatly increased damage, 250% more for bosses. Silence only takes away skills for a fixed four seconds. Break is the bigger damage window; silence is the shorter, simpler shutdown.

Not settled: Whether silence also stops an enemy's basic attacks, or only its skills, is not settled.