I also appreciate what you say regarding the air pressure gradually tapering off. The issue I have with this is there is no other vacuum that I have witnessed which has caused this effect of a gradual gradient of pressure when the barrier is removed. Pressure systems next to vacuums equalize fully when the barrier is removed. So why would the infinite vacuum of space and our pressurized system not equalize and only cause this gradient? Repeating what the text book says really does nothing for us at this point. We need a practical demonstration to the claims that are being made.
So I had an idea for a pressure gradient explanation, I'm going to describe a void or vacuum as just a space that doesn't contain matter, namely air. Its a very simplified version so its not
technically absolutely correct, but I'd have to write a thesis paper if I included all of the thermodynamics of the atmosphere, factored in.
So whether our gravitational model is correct or not, we can agree that there is some sort of attractive force that pulls everything towards the ground. We also know that as you get further away from the earth, that attractive force decreases. Stand on a scale at sea level versus on a mountain, and your weight which is your mass * that gravitational force however you want to describe it, will be lower on top of the mountain. With that, I make the statement that gravitational force decreases as you get further away from the surface of the earth.
We can observe that as you continue to go up, the gravitational force will continue to decrease. Gravity is inversely proportional to the square of the distance. A gravitational force will be 1/X^2 or 1/4th of its original at a distance 2X away. That is a bit harder to allow you to prove to yourself, but it would be possible with a high quality scale and a large enough range in height. Regardless of whether we agree at the rate it drops off at, I think we can agree that at a certain point away from the earth, this force of gravity will be so close to zero, that for all practical purposes, we can call it zero.
I'm neglecting the force of gravity from the moon, the sun, all of the other planets, etc because they are typically minuscule because of how far away they are and that inverse square relationship described a minute ago. All of the atmospheric gases, go from the surface of the earth up to this point where the force of gravity is holding them down to the planet. Typically its referred to as the Karman line. about 100KM above the earth's surface, but that detail isn't important. Around this point, the force of gravity is equal to zero, gravity cannot keep the gases accelerating down towards the planet any further, at this point. Because there are no forces on the gases, and they aren't accelerating towards or away from the planet, they will kind of stay where they are at.
I'm going to explain mathematically with simple integer values, these are more for concept and comparison rather than stating that you have thousands of KG of air resting on your head. Starting from the beach, you have 100KM of distance between the top of your head and all the way up where air is contained. Air has mass ~1Kg/m^3 so say that the surface area of your head is 1m^2, that means that you have 100Km^3 of air on top of your head. If you took the space escalator and went up 50Km above the earth, you'd now only have 50Km^3 of air on top of your head. If we talk about pressure as force over an area, the force is the weight of the air. If you were to get all of the way up to the top, you'd no longer have any air above your head, and no pressure from that air on you. A vacuum is a space without matter (air in our case) where pressure is 0. So you could say that outside of that distance, there is no more air, and the pressure would be 0. In reality, there are gases that escape the earth's atmosphere and drift off into space, but we are speaking relatively here.
A really good example of this without requiring you to travel 100Km up in the air, is if instead of walking up into the air from the beach, instead you walk under water. With the exact same reasoning as before, but now we consider the amount of water on top of your head. Water's density is 1000Kg/M^3 so 1 Meter under water your massive 1m^2 head would feel 1000Kg of water on top of it. Go down to 10m and you have 10,000 Kg of water on top of your head. The pressure increases as you keep going down, and decreases as you get up onto the land. Now the reason I used an easy but absurd value of having a square meter as the surface area of your head, is because it keeps the math simple, but it also helps with the comparison I'm about to make. Lets say you start from 100m under water. Thats only ~360 feet, nothing crazy like 100KM in the previous example. At 100m under water, you'd have 100m^3 of water on top of your head which is 100,000 KG of water. The pressure is astronomically higher than that of 100m above you at the surface. As you swim up, you would feel a difference of 100,000Kg of weight off of your head. If having 100,000Kg of water on top of you was your normal, then not having that 100,000 Kg on top of you would feel like a vacuum. A good example of this is deep sea fish, a lot of deep sea fish like the blobfish, which have evolved to be able to survive crazy pressures like that collapse when they come to the surface of the water, the same way that a human would in the vacuum of space.
Honestly, the conclusion I drew was accurate for an explanation of the concept, but I didn't account for a lot of things like that the air density decreases as you go up, the water density increases as you go down. Gravity isn't the only thing that keeps the air up or down in the atmosphere, etc. But the quantities aside, the idea that there is more substance above your head the lower down you go is correct. That substance has mass that is pushing down on you, creating atmosphere pressure.