First, start with massenkatz' answer above. Then let us change 'comet" to "icy Kuiper Belt Object". Now if we accept what is valuable about this comet is the water, I think we have a possible scenario we can imagine that makes some economic sense.
We are no longer dealing with objects with highly eccentric initial orbits, but we do have the new problem of getting an Icy rock from Pluto's orbit back into the "industrialized space zone" closer to earths orbit. But the water resource is valuable and expected to remain so for generations as water itself is needed by the vast human population for life and the heavy hydrogen isotopes present in the ice are needed for energy production, so governments and companies can take a long view when designing their water supply chain. At any time there will be tens of thousands of icy bodies at various stages of de-orbiting towards earth in a process that takes generations to complete.
They arrive at this: manned or robotic survey ships travel to the belt. They locate good prospects by water/mass ratio, industrial value of non-water content, and viability of revisable orbital dynamics.
They have brought a host of small tugs. These are simple ion drive engines capable of delivering small but constant thrust continuously. They are attached to the target object along with a control module and this package begins the job of returning the object to orbit between mars and earth. Meanwhile, the survey ship moves to find its next target. It has supplies to recover 1000 such objects.
The return orbit of any body is very slow and complex. The ion thrust is very small, so even with an initial boost from another more energetic engine, changing the bodies orbit will take a long time. So, objects use gravity assist whenever possible. First with other Kuiper belt objects, then with planets and asteroids, the planned deorbit involves a series of encounters to first boost velocity and adjust trajectory, then degrade velocity and park the object in an orbit where it can effectively be harvested.
No two deorbits are the same. Companies deploy surveys to take advantage of possible gravity boosts from known high mass Kuiper Belt Objects and outer planets and their moons to return payloads as rapidly as possible using the fewest tugs but only the rarest and most favorable orbital dynamics result in return journeys of less than 250 years.
The incident that eventually sends one of these bodies to earth could happen anywhere along the supply chain, leaving earth with a lot, or almost no warning of the coming catastrophe.