Those are good questions to ask (particularly what the best construction technique is for vertical shafts), but I think your numbers for the elevators are wildly wrong.
Firstly, there should be no real reason for the tunnels to be deeper than about 30-50 feet because sewers and utilities are all concentrated at backhoe depth, which is shallower even than that and building foundations are pretty easy to avoid. The biggest driving factor in depth is probably disruption to the surface during tunelling, which requires staying ~2 tunnel diameters underground. That cuts your elevator time estimates by 2-3x.
Secondly, 1ft/s is really slow, both by the standards of other elevators in the world and in comparison to their own demonstrated prototypes. The car elevator they demonstrated in July 2017 appears to move around 3-5ft/s once it gets up to speed [0], and I expect that number to only increase, particularly if the shaft gets deeper. Human elevators reach speeds up to 50ft/s in tall buildings, and while there's no need anytime soon for the Boring Company to hit those kinds of insane speeds, there don't seem to be fundamental reasons they couldn't if they needed to.
Combined, those factors imply your numbers are close to an order of magnitude off, and imply a reasonable number of elevators in the 30ish range. There are real challenges they need to solve, but I don't think elevator times or count are one of them.
>Firstly, there should be no real reason for the tunnels to be deeper than about 30-50 feet because sewers and utilities are all concentrated at backhoe depth, which is shallower even than that and building foundations are pretty easy to avoid.
Well, this assumes a flat geography. At highway speeds, nobody likes steep grades in either direction, so at the top of a hill, you'd need a deeper elevator to get to the tunnel network. Today's metro systems also prefer to move people down to the trains with escalators or elevators at hilly areas.
>Combined, those factors imply your numbers are close to an order of magnitude off, and imply a reasonable number of elevators in the 30ish range. There are real challenges they need to solve, but I don't think elevator times or count are one of them.
Even if the elevators teleported you to the tunnel, there is still a loading and unloading time involved. This is true of human transporting elevators as well.
It takes 9.5 seconds for an average car, say a Toyota Corolla, (https://www.caranddriver.com/toyota/corolla) to accelerate onto the highway today. The elevator needs to beat that time (loading, accelerating to move down, decelerating, unloading, and accelerating into the tunnel network itself) or throughput is no better than on a standard highway. And on an on-ramp today, cars don't have to wait for the other car to fully enter the freeway.
I pulled my numbers for vehicle elevators by looking at the website of someone who sells vehicle elevators (which said 30-120fpm). Vehicle elevators are slower than human elevators, partly because vehicles are much, much heavier. I suspect most vehicle elevators are going to have to be hydraulic drives, not cable-driven. There's also acceleration to worry about, but short elevator spans are not going to let you build to full speed anyways.
Depth is trickier to reason about. The Boring Company's FAQ explicitly states that "There is no practical limit to how many layers of tunnels can be built, so any level of traffic can be addressed." This suggests that they generally want multiple layers of tunnel. As a matter of practice, most major cities already have underground rapid transit systems that already occupy space. As you go higher, you have to worry about the complex geometry. Because of the inherent lower capacity of the system, you also need an order of magnitude more tunnels, which is going to push you deeper anyways.
Even if you think my numbers are close to 10× off, the capacity advantage of rapid transit is still looking closer to 10×. The advantage of transit over SOVs is simply that large.
[0]: https://youtu.be/9jvD_dFA44g
Combined, those factors imply your numbers are close to an order of magnitude off, and imply a reasonable number of elevators in the 30ish range. There are real challenges they need to solve, but I don't think elevator times or count are one of them.