Meanwhile, here on Earth, we have billions of cubic feet of helium gas underground with infrastructure for liquefying it, we have access to conductive and convective cooling for our heat pumps with the whole thermal mass of the Earth to sink heat into, and we have all the industrial infrastructure and construction and maintenance infrastructure right here.
Oh, and if your datacenter is in Palo Alto instead of on Pallas, you have the added bonus that you don't have to worry about networking with a 15-minute ping.
tl;dr space isn't cold, vacuum isn't a great cooling medium, and shipping is expensive.
11km/s would be ca. 40000 km/s, in other words earth to moon in 10 secs.
By the way, if the ship is surrounded by fuel, ie. in Jupiter's atmosphere, it could use quite a lot.
However, I did actually mean to type km/s. Earth's escape velocity is, in fact, 11.2 kilometers per second. (Around 25,000 mph)
Oh: To clarify, "Escape velocity" is the speed you need to escape Earth's gravity well entirely, so that you are no longer orbiting the Earth at all; it's about the amount of velocity you need to go on interplanetary missions. If you just want to go to, say, the Moon, then you don't need to go that fast. If you just want to go to low Earth orbit (LEO), then orbital velocity's only around 7 km/s.
But that isn't "peak speed" or anything, that's just ... how fast you have to go to be in low Earth orbit. The International Space Station is traveling at 7.67 km/s right now.