It depends on how you define "point shooting".

I will practice shooting from a close in retention position starting from a draw at ranges of 1 to 3 yards. One of the things I focus on is keeping the support hand high and close to the chest. That's important to develop muscle memory that keeps the support hand high, so that if you ever need to extend the support are outward to create some space or ward off an attack, the hand will stay above your line of fire.

That said, I also practice side stepping and pivoting while at least pointing if not actually shooting my pistol (it isn't something you can do at a range). If I am ever charged by someone with a knife, I have no plans to stay on the X but rather will let the assailant's momentum carry him past as I side step to the side, pivot and continue sidestepping 90 degrees away from his line of advance as the tries to turn into me. In the 5 or 6 seconds it will take him to actually close to a close in retention distance, I'm going to be shooting him multiple times from an isosceles stance and then if he is still closing pulling the pistol back into a close in position.

If we are talking about ranges beyond 1-3 yards then I see no value in "point shooting" if that is defined as not using the sights. Yes, I know that about 80% of LEOs report never looking at the sights, even in longer range shoots. That doesn't mean sights are useless in a self defense shoot, it means most LEOs are poorly trained and or do not practice enough to master the use of sights or their services weapon in a stressful situation. Ignore the sights in a real world shoot is one of the primary reasons that LEOs in real world shoots perform poorly at even short ranges of 5-7 yards and perform abysmally at ranges over 7 yards.

It takes a lot more time and practice, but it also makes a lot more sense and results in equal speed and greater accuracy to learn to raise your pistol to your line of sight and as the front sight comes on target to pause and ensure the rear sights are aligned before firing.

(If the rear sights are not even close, or if the front sight is too low to even see, then you need to back up a step and select a hand gun or perhaps a new set of grips that actually fits your hand. You should be able to look at the target, close your eyes, bring the pistol up then open your eyes and have the front sight on target and the rear sight in the general vicinity of the front sight.)

Once you have paused and tweaked the sight alignment, hold the alignment while you finish the trigger pull. You'll start out slow but as you practice and as you develop your grip, the muscles in your hand and arm will know exactly what they need to do to create the sight alignment. At the same time your trigger finger and hand will also learn how to complete the trigger pull without significantly disturbing the sight alignment.

After awhile you'll find the pause is indeed only needed to verify the sight alignment, not correct it. At that point you can start picking up speed and essentially only reference the front sight and it's position on the target.

Once you are shooting accurately at speed, the "pause" is really only a small fraction of a second where you are verifying the need to shoot once the front sight is on target. By that time you'll have put a few thousand rounds down range, but you'll find you are shooting just as fast and with far greater accuracy than if you were "point shooting".

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Edit:

I want to make it very clear that no matter how good or bad police officers shoot when pursuing an armed suspect, going to slide lock reloading and shooting some more, and in the process skipping bullets all over the neighborhood, you as an armed citizen literally cannot afford to do that.

When an officer does it, he's doing it with the backing of department's 1) policies, 2) attorneys, 3) liability insurance, 4) in many cases sovereign immunity, and 5) a great deal of latitude from the courts on things such as "mistake of fact" shootings.

Those are all things you as an armed citizen do not have. When an officer hits an innocent bystander, but is otherwise within policy and the limits of the law, it's a tragedy, but the officer isn't going to jail and probably isn't going to even be reprimanded unless he used really poor judgement getting into the situation in the first place.

If you tag an innocent bystander, there's a very good chance you are going to jail and even if you manage to avoid jail, you're going to get sued in civil court, where you will lose and receive a judgment that will probably bankrupt you and your family.

If you really plan to use a hand gun in self defense, then learn to shoot it well, shoot it a lot and when ever you can shoot it in situations that involve stress, time pressure and movement that will better reflect real world self defense shoot conditions.