Monovision is a popular method of maximizing distance and near vision after cataract surgery by selecting different intraocular lens powers for each eye. As you seem to understand, one eye (usually the dominant eye) is focused for distance and the non-dominant eye is focused for near vision (reading or computer).- MDA

Crossed monovision may be as effective as conventional monovision

Certain patients may respond better to the standard technique.
Crossed pseudophakic monovision for patients with a mild degree of anisometropic pseudophakia may work as well as conventional pseudophakic monovision, but crossed pseudophakic monovision has more contraindications and should be avoided if the conventional technique can be performed in most clinical conditions.
IOL monovision is one of the best ways to handle presbyopia in cataract patients. It is a predictable and tolerable procedure, which results in good vision quality at a low cost for the patient, Fuxiang Zhang, MD, told Ocular Surgery News.

Just as effective

However, in a study, Zhang and colleagues showed crossed pseudophakic monovision is as effective as traditional monovision for patients with a mild degree of anisometropic pseudophakia and should be added to the ophthalmology armamentarium.
“Biometry is not perfect, and we all sometimes miss our refractive target. If that happens, crossed monovision may become necessary if the patient still wishes to be glasses-free. For example, if we operate the non-dominant eye first aiming –1 D for near vision but end up as –0.25 D with good distance vision and the patient is happy with the operated eye as the distance vision eye, we can still do the second eye, the dominant eye, aiming at near,” Zhang said.
Additionally, patients sometime want to have the second eye cover what the first eye is not able to see well without glasses. In these types of situations, Zhang said crossed monovision can be an effective technique….
Source: Healio