The trouble with "letting the Police do their job" is that in the precise spot in which you happen to live, or used to live, their job probably won't start, if it ever does start, for about a week. In the meantime, letting the Police do their job means letting the damn looters and arsonists do their job, without anyone laying a finger on them, laying a finger on them being illegal. This is a doomed policy. If most people are compelled by law to be only neutral bystanders in a war between themselves and barbarism, barbarism wins. The right to, at the very least, forceful self defence must now be insisted upon. The Police, as we advocates of the don't-disarm-the-victims-of-crime policy have been pointing out for decades, can't be everywhere. They cannot instantaneously attend every crime, and magically prevent it. Only the potential or actual victims of crime can sometimes immediately prevent or immediately punish crime, provided only that they are not forbidden to.
I recall reading about a yob who stole something from a street stall in Nigeria, many years ago. He was promptly set upon by a mob, of stallholders and their customers, and beaten up. Are you civilised? It depends which side your mobs are on. All our mobs, except the little mobs that are the Police, are anti-civilisation.