Most wheels are mounted on (ball or roller) bearings. For speeds approaching 1000 mph (whether practical or not), solid
aluminum wheels seem to be the popular choice.
I have a different approach to this, regarding design. My idea is to have a thin hoop act as the wheel, rotating about a
hub that doesn't rotate. Regarding bearings, a "plain bearing" approach would be utilized. Between the wheel and the hub would be a layer of liquid that acts as a lubricant and coolant.
This liquid would be pumped at an impressive rate, as a "total loss" system. This means that it would leave the vehicle
and be absorbed by the local environment. The liquid might consist of something like a mixture of cold brine and soap.
It could be colder than 32 degrees F, and slippery. The amount required might be significant for a land speed attempt,
perhaps in the neighborhood of 50 gallons per run (of about 10 miles or so). Of course, the chemistry of this mixture
should be relatively friendly to the environment.
The advantage of doing this could be in the design of the wheel. With less mass rotating, less kinetic energy would need to
be developed in this rotation. Since a large continuous solid wheel would not be rotating, the strength of the material
should not be problematic. I envision a wheel made of alloy steel (perhaps alloy 4340 or something similar), perhaps about 1/2" thick. The (non-rotating) hub could be aluminum, flowing a huge amount of this lubricant. Yes, a lot of testing would be in order, to prove that this could work. Yes, it's expensive. But at least the wheel is not likely to fail due to stress related to the rotational speed.
I imagine a bunch of testing could be done, on vehicles capable of lower speeds (say, starting at about 200 mph). After
a run, measurements relating to wear could be taken on the wheel. It's only money, right?