The above comment comes from a professional Okapi keeper and is thus the comment holding most value.
The Okapi inhabits dense rainforests of the DRC, not the grassy plains of East Africa. Hence, letting the grass grow high doesn't give visitors a good idea of its natural habitat.
How does mowing a paddock break the parasite cycle if the animal is still being run on it?
Allowing the enclosure to become overgrown may result in calmer animals, I do not know the disposition of the current Chester okapis, or how much behavioural training they have had.