Not generaly for a couple of reasons:
First is most places are rather restrictive concerning concealed fixed blades. A fixed blade can be employed immediately in a very smooth motion during a struggle, much easier than even a firearm. It will not get caught on any garments and only the motion to remove it and then deploy it are necessary to put it into use. When in use it will then not result in a bent blade (if well made) or a lock failing while encountering bone or force exerted on the blade from directions it was not made to handle.
Yet because thier use and especialy concealed carry is restricted in most of the nation, especialy those with decent length, they won't be available to most.
Folders, even impressive seeming ones are nowhere near as ideal as a fixed blade. They tend to require some additional movement to deploy as well. I have some nice folders and can deploy them rapidly all day long when my wrist can move and I can hold them in a loose grip. Certainly looks impressive and intimidating.
Once already in a struggle, possibly fending off another weapon being used against me is another story. That very simple flick of the wrist when rolling around on the ground is not as easy, especialy after retrieving it from a pocket while trying not to sustain injuries from someone using both hands and or a weapon to attack you.
Before an attack or in an offensive manner (aiding someone else I hope)? Sure, take half a second to remove and deploy. Once grappling? Not as easy.
The small amount of time it can take to retrieve it during a struggle can also be the brief second your opponent needs to gain the upper hand as well if they are relentless with no pauses.
Once deployed many folders are also only good at applying force from a couple angles. The locks can fail, resulting in trouble or even self inflicted injuries to your hand or fingers when encountering bone or violently moving muscle that applies force against the design of the blade.
The law also limits blade size to quite small many places.
Fine in skilled hands when targeting specific areas, especialy in demonstrations against people not fighting for thier lives or deploying a weapon themselves. However in an actual struggle resulting in grappling where the opponent is constantly trying to attack with a weapon or secure your weapon or weapon hand, slashing attacks are harder to deploy than stabbing attacks. Stabbing attacks against the least defended and most acessible parts of the opponent's body without at least a 5-7" blade are ususaly not going to reach vitals. So they may result in a lot of blood and gruesome looking wounds, but may not stop the fight of a determined or skilled opponent. There is many vulnerable areas to small blades, but they are far easier to attack in a dojo during training than against the thug beating you with a blunt object, stabbing you, or trying to free his firearm from your grasp, or get it pointed in your direction to fire.
They can be good for retention purposes with a firearm, allowing you to slash with your offhand at any limb extended your way. Yet if you are deploying deadly force, then the opponent probably is armed. If they are armed and continuing to come at you while you have a gun in your hand, slashing at them with a knife is probably not the ideal action.
So the law ususaly limits knives to folders, and usualy of lengths that are not ideal for stabbing attacks. Slashing attacks against someone putting up a good fight are not as easy as during training or demonstrations, and vulnerable positions harder to reach without receiving damage yourself.
If you are deploying deadly force I assume the opponent is armed, or there is a great disparity of force. If they are armed, especialy with a more effective illegal weapon (they are less likely to be following the law) than you, then be prepared to receive injuries if attacking with a short folder. Only a skilled individual will reliable disable an opponent with a short bladed folder. Unskilled will result in gruesome but ususaly survivable and not incapacitating wounds. People living with dozens of 3" stab wounds is quite common.
Even the unskilled can reliably inflict serious wounds stabbing with a long blade. The skilled can do so more effectively. But such blades are often illegal.
So if the law limits you to a short folder, expect to take some injury against an armed opponent before they are down, and then only if you know what you are doing.
The second reason I would rather not deploy a knife is society is less understanding of what they cannot relate to. Someone in fear of thier life pressing a button, or pulling a trigger is something even the housewife on the jury can ususaly relate to.
Repeatedly stabbing and slashing with blood flying everywhere while you systematicly tear down your opponent's body they cannot. Tearing your opponent apart with slashes from a short blade also takes more intentional thought and a mindset that sounds savage in a court room. Aiming COM and dropping an attacker takes far less thought and seems far less sinister and systematic.
You could stab someone dozens of times in a couple seconds if you are strong and quick, but in a court room dozens of stabbings sounds very excessive and unnecessary. Someone who has not been in a knife fight will not understand the amount of injury the human body can tolerate before it is incapacitated when seconds count and you need them stopped NOW.
As a result self defense with a firearm is far less likely to result in you being found guilty at trial than using a small knife is. A few rapid shots seems far less excessive than dozens of stab wounds. Even if you only did what was necessary to incapacitate and stop the attack.
Further it is also easier to use less force, back off and have the ability to use more if necessary with a firearm.
Using less with a blade than is necessary and backing off can then result in the tables turning and losing control of the fight. Yet in court that will not matter. If you use a blade, have control of the situation, and then cease the attack, and then the opponent uses that opportunity to take control of the situation it can result in your death.
Giving up your advantage in a knife fight that may not be over is much more serious than firing fewer shots, and then firing more if necessary.
If you do not give up your advantage after gaining control in a grapple involving weapons it will seem excessive in court, and much more likely to result in prison time for you.
So a gun is clearly better. Not just for effectiveness, but because in court it is cleaner and more jury members will be able to relate to its use in stopping a lethal threat. The soccer mom on the jury might have a harder time as the prosecutor describes the multiple stab wounds, the intentional thought and the graphic successively inflicted knife injuries. They will be less likely to understand the speed at which multiple knife wounds can inflicted than the speed at which a gun is fired.
The same self defense with a knife is much more likely to result in long prison time (and loss of your rights as a felon) than with a gun.