The Zubrin-Baker plan of 1991 suggests using a tethered weight, rather than having a ship of huge radius.
e.g Have your craft attached to a weight on a cable some hundreds of metres long, giving you a long effective radius of rotation.
Z-B imagined this for being in use in transit to and from Mars: fire it up using minor rocketry on both the craft and the ballast for the journey at 0.38 g to get folks enured to Mars gravity on the to-journey, then dispose of the ballast prior to Mars landing. On the return journey, you could start at 0.38 and ramp up to 1.0 g and then again discard the return vehicle’s ballast before entry.
There’d be no reason you couldn’t use such a system in Low Earth Orbit though. If you needed to dock you can fire the rocketry to slow and stop the spin, then after you’ve finished, fire it up again.
I’m sure a lot of astronauts would prefer to be able to use the toilet like a normal person…
In the example below, the effective radius of rotation at the centre of the craft is 100 metres. The red dot is the centre of mass. There would be a small variation in acceleration around different parts of the craft but not excessively. To obtain a Mars gravity you’d need a rotational period of around 32 seconds.

To be honest I’m a bit disappointed that no one has done this in LEO to find out the effects of reduced gravity on the human body. We have years and years, about 150 person-years, of data of the effects of zero gravity (or technically microgravity) on the human body, but nothing at all on the effects of 0.38 g, or 0.16 g.