The personal moral outrage we feel and the desire for certain harsh punishment to be applied in these cases is human nature.

One reason we (in the USA at least) have a government of checks and balances, and a court system that reflects that sentiment, is to prevent the power of the mob from being harnessed unjustly. The short term gain from making a public example out of evil criminal behavior has the potential to cause serious long term consequences if those tools against malevolence ever get wielded by the malevolent themselves. Then we will spend or suffer far more blood overcoming those malevolent actors than was ever saved by making an example of the initial malevolent few. If you look at this as a cyclical trend, we as a society have certainly already progressed down this road to some degree and we'll suffer both more consequences of enabling these desires, as well as suffering the consequences of trying to fix them in the future.

Due process, constitutional punishment and the rule of law is costly to endure. But I think we need to endure it, especially when confronted with addled brains such as these.

Unfortunately, we are dealing with humans that are clearly beyond redemptions in a non-religious sense of the word.
I do agree with you that as a society we got less violent for a while after we banned public displays of grotesque cruelty. But it seems like something broke after the Floyd riots. I am not sure what needs to be done as a non-trivial part of our population has become increasingly feral. Like the perps in this case. I really don't think that kindness is the answer here. There will definitely be more of that.