This method of correction of presbyopia is called monovision.
Monovision is a method that has long time preferred young, beginning presbyops, who want to see well at distance and also for near without changes of eyeglasses correction. It is not seeing only with one eye. The dominant eye is fully corrected for long distance and the second eye corrected for near, which is in binocular vision more or less suppressed.
While monovision may lead to a lack of focus on a very large and very close distance and initially takes some time to adapt, to patients is commonly prescribed, especially for its simplicity and high initial success.