It has to do with the time set aside by God where He will reckon with the evildoers on Earth. In the meantime, His great grace prevails and falls on the unrighteous along with the righteous.
That said, it doesn't mean that people will not suffer the consequences of their sin. That is the nature of sin. It is destructive. That's not Gid's punishment or judgment.
Perhaps a revelation of God's grace is necessary.
Your explanation of judgment doesn't deal with the lesson of the tares. I'll summarize it to make my point. Every generation is composed of people for God and against God. Often folks wonder why God doesn't just eliminate all opponents of his truth since he knows who they are. The main problem is there's often little if any outward difference between possessors of truth and pretenders. Indeed, the grace of God is available, when activated through faith from a sinner to change any of the pretenders to become his child, holding his truth. So were are commanded to preach the gospel of Christ so the pretenders might be convinced of their error and be born again from above.
Leaving the tares in the field means God lets the sinners remain as an overwhelming majority versus Christians, but also commands the righteous to be separate from them. The reason for separation is that like the farmer could prepare for harvest by easily separating the poisonous tares out on the first day of harvest. Some of the desired crop right next to the evil plants might be uprooted by the entangled tare roots, but the good seed on the damaged good plant can still be harvested, having already matured. An example among people could be a beloved spouse being a tare, that when separated in that future judgment of Christ, might be a painful experience.
The tare species can be controlled somewhat while weeding the rows by breaking the main stem, preventing it from competing with the wheat. With it's seed head on the ground, the wheat seed remaining high helps harvest the good. We break the power of the devil by submitting to God and resisting the devil, casting demons out, but admittedly very little of that happens in the modern Churches today.
The parable has to do with each generation of the Church until Jesus is back on earth. We know many people merely claim to be Christian, that mostly are of no help to the Kingdom. Some invent false doctrine, often simply out of ignorance of the true doctrine. We ought not go about burning them at stakes. Instead, we have instructions concerning the tares. We are mostly to avoid the bad, though when opportunity strikes, witness truth to them.
Romans 16:17-18 (KJV)
17 Now I beseech you, brethren, mark them which cause divisions and offences contrary to the doctrine which ye have learned; and avoid them.
18 For they that are such serve not our Lord Jesus Christ, but their own belly; and by good words and fair speeches deceive the hearts of the simple.
We teach our babes in Christ to avoid sampling the poison of sinners. Moreover, we learn not to be friends with the world. Even more, we ought not even share a meal with someone claiming to be Christian that lives in open sin.
How we, Christians, are supposed to co-exist with evil is the main point of the parable of the tares. We know that those sinners holding out to face the judgment of Christ will be separated out from among the Church when Jesus comes back. Knowing that we know the immeasurable value of persistently producing good fruit while in this world.
Sin does have consequences, so slight, some terrible. They often come upon the sinner in the form of damaged health from abusing the body or mind. Those are mostly natural processes, requiring no administration from angels or God.
Punishment for sin in this life and at the Judgment do require administration from God, or his authorized ordained ministers of law, our police, detectives, forensic scientists, prosecuting attorneys, judges and juries who deliver judgments for criminals. We could say receiving punishment through justice is a consequence of sin. In that sense all justice and judgment in this life and the next is a major consequence of sin. There's a big difference, though, that while in this life a person might benefit from God's grace through repentance and believing the gospel of Christ, avoiding that terrible eternal consequence, but maybe having to retain the temporal consequences, such as living in a prison.
Rom 13 describes how God has given man authority to judge offenders. That passage isn't saying the same as the Matthew 13 tare parable. Rom 13 covers civil judgment from law ministers operating from God's direct authority to judge and punish, whether Christian, Hindu or atheist. It isn't to say God never judges during the here and now a person, family, city, state, nation. He is on record as having judged man many times, punishing them still like leaving Israel mostly blinded to the gospel even now regardless of how clean their lives are. The Jews are still under judgment of God, which for some in the last days will end with mercy and grace.