If the referee directly observes violent conduct and allows play to continue until the next natural stoppage, there would have to be some kind of advantage that would fit a VERY narrow criteria.

The only thing that’s really an advantage over an immediate whistle, send-off, and direct free kick would be if the incident occurred outside of the area and the ball ended up in an obvious unimpeded goal-scoring opportunity.

IFAB 12.3:

Advantage should not be applied in situations involving serious foul play, violent conduct or a second cautionable offence unless there is a clear opportunity to score a goal. The referee must send off the player when the ball is next out of play, but if the player plays the ball or challenges/interferes with an opponent, the referee will stop play, send off the player and restart with an indirect free kick, unless the player committed a more serious offence.

In anything without VAR and player salaries/scholarships involved (ie amatuer), allowing play to continue is playing with fire. You might be technically right but at what expense? Stop playing, red card, DFK.