Currently, the crust varies from 4km (oceanic) to 10km (continental) to 30km (mountains).
How would the earth be different if it was all 1/4 the thickness? So it was 1km, 2km and 7km?
Would we have more volcanoes / earthquakes / geysers?
Would the crust be any warmer? Would life be different?
I'll play along... Let's go the mind-experiment path.
Since the crust, as is, makes up such a small portion of the Earth's structure, reducing that by, let's say, 3/4 would not be that big of a change.
A change the the outer-most surface layer thickness would have relatively little impact on the overall function of the mantle on a macro-level.
The surface would be thinner, which if we project out, we might think that this means there might be more magmatic activity. I suggest (unscientifically) that that might actually not be the case. Remember that pressure of the crust and surrounding material contribute greatly to the development of magma, by reducing the crust's thickness, you are thus reducing the pressure.
Reduced pressure would mean that magma would likely have to form a little deeper into the mantle than is currently normal. Since the crust is thinner, the distance to the new magmatic layer is roughly the same distance it was previously. Thus, by thinning the crust by 5km, you've pushed the magma-bearing layer down by roughly the same distance.
In the grand scheme of things, really, such a change would be negligible, and the natural forces that exist now would still be in play, thus the system would stabilize itself, and even rebuild the crust to some degree over time.
The surface changes to such a thin crust would have only superficial results, including:
Earth would be livable, and not a lot different than now.
The real question becomes, then, why is the crust to thin?
Any "catastrophic" disruption of the status-quo would lead to severe consequences.
If the crust slowly "erodes" to this thinness, life would have plenty of time to adjust to the changes.
If the crust used to be thick, then where did that material go? Did it get subsumed into the mantle somehow? Did it get ejected into space? Each of these answers initiate a wide variety of new questions.
To answer the question of the resulting air pressure, we have to know why 75% of the crust is missing. It help's to know what exactly is the crust. The crust is the surface portion of the planet that is chemically differentiated from the layer below it (the mantle). This is largely considered to be primarily the output of volcanoes that has not been recycled back into the deep.
Case 1: The earth's crust is thinner due to natural causes.
I will simply assume that reduced volcanism is the only reason. If so, we also remember that volcanism is considered the likely source of most of earth's atmosphere. In this case, the atmosphere is considerably lighter and pressure is correspondingly smaller. Since 75% of the crust is missing as a first order guess 75% of the atmosphere is also missing. Lots of things not good, but humans won't be around to notice. Large mammal biology are just too hard to maintain at the reduced oxygen levels -- we are well into the death zone of low oxygen pressure. The reduced pressure obviously cause lots of changes to the locals.
Case 2: The earth's crust was taken by aliens less than 1 million years ago to make some nice rock gardens -- asteroidal rock just does not have that same igneous look and feel. Being environmentalists, they take their 75% cut using magical tech levels that do not disturb the crust any more than necessary so as to not upset the locals. I.e., we can assume crust is just as we find it today, just that 75% of it is missing. This sounds more the the actual question intent to me.
The atmosphere is unchanged, i.e., the same mass of O2, N2, etc. still in the sky. So how is pressure affected?
The earth's radius is slightly smaller, assume it to be 1% (60 km) as an average number. Because Earth's surface area, being proportional to radius squared, is now just over 2% smaller and thus pressure is 2% higher.
But we are not done, the earth's mass is reduced and the radius is smaller, changing the gravity. Can we figure out the net effect without the hard math. Surface gravity is proportional to mass and inversely proportional to radius. However the earth crust is only around 50%-60% of Earth's density (the real number are uncertain), so the mass decrease is only about half of what would expect. We will ignoring the difference in the gravity gradient due to crustal loss (I promised simple math). In case you are curious, I know I can ignore the different gravity profile because nearly all of the atmosphere is very close to the surface -- so gravity is very nearly a constant value for the bulk of the atmosphere and the difference in gravity profiles (rate of change) can safely be ignored. If we did the math is would actually slightly decrease the pressure as the rate of gravity decrease would be higher.
Plugging in 1 * m/(r**2) = 1 * 0.995 / (0.99)* is about 1.015, i.e., atmospheric pressure is about 1.5% higher
Combining the effects from gravity and reduced surface area, the surface pressure is little more than 3.5 percent higher overall.
Tired last night and I did not finish and did not catch that I wrote 6 km for 1% of the earth's radius.
Note that actual average crustal thickness is about 12.5 km (70% ocean with the thin crust 7.5 km thick and 30% thick crust 25 km thick -- sounds like something from Pizza Hut), much less than the 1% assumed above, so the real effect on air pressure is simply not significant. Using the real numbers make the pressure changes less obvious. Using actual numbers for the crust, the net atmospheric pressure is only about 0.5% higher. This is the about same as the difference between sea level and 35 meters.
Air pressure is relatively easy to figure, the other effects already mentioned are considerable more difficult to actually compute. For example, assuming case 2 how does heat transfer from the core change and what is the effect on temperature, etc. As a first approximation 25% crusts means 4 times the heat transfer rate. But based on what. Well, the crust boundary is the Mohorovičić discontinuity. At the Moho layer, temperatures at 150-200 C under the ocean and 500-600 C under the continents. The Moho layer will cool somewhat due to higher heat flow, but just how much is hard to say, unknowns are fairly large.
In this case, quadrupling the average heat outflow does actually not matter much because it is so small. -- Average is about 0.1 watts / square meter a small fraction of solar flux.
However, even this changes overlooks an important change. 4 times the heat flow means that temperatures increase as you drill / mine the crust at 4 times the current rate. Some gold mines already require air conditioning to be livable, the problem would be much more severe. It would make mining more expensive, and prevent our deepest mines. Oil drilling would be effected, not because of overheated miners, but because the higher temperature weaken the drilling equipment and more importantly break down drilling fluids. Some deep oil wells are over 1500 meters -- the higher temps would probably make this impossible, certainly much more expensive and economically unjustified.
It is very hard to correctly evaluate all of the changes resulting from even a relatively minor change.
