Besides the immediate threat of mass rioting and an armed resistance no matter who you're flogging, public torture as entertainment is a very, very bad precedent to set, and only serves to build up a culture of antipathy. Imagine how the wider justice system would change once that's normalized.
Going by that the answer is that Authoritarians will all double down to the point of seeking out authoritarian buffer states because now they believe that the democratic world is either conspiring to get them or a motivator to their people to kill them just by existing at all.
As others have said, seems like it would have a counterproductive effect.
Punishment or inflicting pain tends to engender sympathy for the one being hurt.
That said, sometimes political assassinations have been effective based on the criteria of the assassin. I'm reminded of the guy in Japan who shot Shinzo Abe.
January 6th is a reference to a failed insurrection instigated and coordinated by those same authoritarians that has been so insufficiently punished that it may as well be called a practice run.
A proper response would have been to send in the national guard, corral all the insurrectionists and put them in a camp to await trial there.
Speedy justice, all with insurrection and murder/felony murder as the basis for their charges.
Then you figure out how to work through the backlog of prison sentences. Maybe use an island for that or something. Far away from mainland US like Guam.
There you provide food, housing, schooling and allow them a chance to become productive members of society after their sentence.