The biggest expense was installing the mantle ducts to keep the carbonate-silicate cycle operating.
The comic displays a cross-section of a subduction zone, with an anchor bolt connecting the two tectonic plates. Sudden shifts in the positions of tectonic plates relative to each other is a major cause of earthquakes, especially the largest ones. Anchor bolts are used to secure an item in place, for instance to attach a building to its foundation. In earthquake prone areas, anchor bolts are often used to secure furniture so it won't slide or jump around during a tremor, potentially creating a hazard. The joke is that, instead of settling for an engineering solution that minimizes the consequences of an earthquake, geophysicists have applied the solution to prevent earthquakes from happening. The caption facetiously expresses frustration that the geophysicists have taken this long to address the earthquake problem at its source. The simple infeasibility of this project is another part of the joke.
Subduction is a geologic process in which two plates of planetary lithosphere converge, and one is dragged under the other. The Earth's lithosphere is divided into tectonic plates. They slowly move across the surface at a few centimeters per year, although the rate is nonuniform across plates. Where they collide, the denser plate gets dragged under the less dense plate, in a process called subduction. Earthquakes are common at subduction zones, and subduction can also lead to volcanic activity. An "anti-subduction anchor bolt" would aim to stop the process of subduction and the movement of plate tectonics as a whole.
A round head bolt is screwed in through both the oceanic lithosphere and the continental crust from the bottom up, with a plain washer on either side, and a wing nut tightened at the surface. Washers are present to prevent the bolt and the wing nut from sinking into the crust, by distributing the forces over larger areas. There are several concerns not addressed in the comic with such a design. The implication that the bolt is being screwed in from the mantle side would imply that a very large bolt head was operated from inside the mantle. (There are types of nut-and-bolt system that might be easier to deploy, such as toggle bolts and mollys. These would have the bolt head on the Earth's surface, rather than in the mantle, and use a spreading "nut" inside the Earth. They wouldn't require conducting enormous operations from below, "merely" a large hole bored from above.) As of the time of posting of the comic, humans have not drilled a hole through a continental crust, still less deployed large vehicles in the mantle. In addition, the presence of wing nuts, fasteners that are designed to be able to be screwed in by hand, implies work done by a larger being that has appendages able to use the wing nut. The bolt itself would be a technological challenge, as well. It would need to be made to withstand the temperature of Earth's mantle, around 1000°C near the surface. At these temperatures, most commercial stainless steel used to manufacture bolts would experience noticeable strength losses. The bolt would need be around 50 km long. Moreover, as subduction zones move parallel to each other, the construction would have to withstand high shear forces, something that a bolt is rather unsuited to compared to other tools, such as rivets. On top of that, ways to alleviate stress must be sought out as if the bolt fails, it could produce a highly amplified earthquake. On top of all this, having secured the bolt, the mantle team would have sealed off their most obvious route of exit back to the surface.
In the short term, earthquakes and volcanic eruptions are typically bad for those living nearby, and thus ways to prevent them happening might reduce economic risks in those areas. However, volcanic eruptions deposit nutrients in the surrounding area, enriching soils. Volcanos also release gases. The vents mentioned in the title text might replenish the nutrients and gases, replacing the benefits of eruptions. Earthquakes sometimes trigger tsunamis, which create or modify beaches, and redistribute nutrients from bays and estuaries across coastal plains. So, while the immediate effects of eruptions and earthquakes can be disruptive, they also enrich the environment. Areas at risk from these "disasters" are also attractive and enriched as a result of these same events.
When plates collide but do not subduct, they often uplift, thickening or raising the crust. The Himalaya mountains, are an example. Tectonic plates spread apart as new lithosphere is formed at ridges, most of which occur under oceans. If spreading continued, but subduction was prevented by the system of anchors pictured in this cartoon, there would likely be new areas of uplift. If positioned appropriately, the mantle ducts, mentioned in the title text, might slow or stop the spreading, reducing uplift.
The title text references the carbonate-silicate geochemical cycle. Briefly, subduction and subsequent heating of the global crust restores carbon dioxide and silicate rocks to the planetary surface, countering the effects of carbonate deposition and silicate rock weathering. Anchor bolts sufficient to stop plate tectonics would also stop the carbonate-silicate cycle, leading to unexpected, and likely unwelcome, changes in the surface geosphere and biosphere. (Arguably, if the carbonate cycle alone could be paused, it might be a means of reducing the amount of carbon dioxide in the biosphere.) To restore the cycle by an unknown mechanism, "mantle ducts" have been installed as part of the planet-wide plate anchoring system. It is stated that the mantle duct installation was the most expensive part of the project, implying greater intellectual and technical challenges than the already-massive ones associated with anchor-bolt design and deployment. It is unclear how these mantle ducts would operate in a way that does not replicate many of the issues that the anchor bolts were intended to solve.
This project would presumably render Beret Guy's subduction license worthless.