"We should just execute them and save money" is instigating violence.
If you aren't willing to spend resources because it's "obvious" to you, you do not care about Justice.
Cops always think they got the right guy, and they are regularly blatantly wrong, including for people on death row.
That's why we have trials, with independent judges, juries and rules.
Remember when the Boston marathon bombing happened, and Reddit users identified dozens of different people as obviously, and definitely, the bombers (https://www.cnet.com/tech/services-and-software/reddit-regre...)? Remember when the LAPD opened fire on multiple random civilians who they thought might be Christopher Dorner (https://en.wikipedia.org/wiki/Christopher_Dorner_shootings_a...) remember when the DC sniper was active and the tip line received thousands of calls from people claiming to have 100% certainty that they saw the sniper, then describe people of conflicting races, ages and physical descriptions (https://en.wikipedia.org/wiki/D.C._sniper_attacks)
We have trials so that we make sure we put the bad guys in prison, not random innocent people who were misidentified. They're for the benefit of everyone else, not for the criminal.