You propose a really good idea, but I'm not aware of this being put in place anywhere.
Some streets will be green wave in one direction, the direction of dominant flow, e.g. westbound in the morning and eastbound in the evening. (I know this is done regularly on Northern Blvd in Queens, NY, especially to help out with traffic from NY Mets games.) And where this is done it will typically be done on multiple parallel streets. But this leaves no alternative for those travelling in the reverse direction.
In Los Angeles, there is near equal amount of traffic between the Westiside (Santa Moinica, Westwood, and Century City) and Downtown LA. There was a plan to make the two parallel E-W streets Olympic and Pico to each be 7 lane one-way monsters of traffic. This was not too popular with residents. They preferred to keep each street two-way. Plus, at times Pico and Olympic are nearly 1/2 mile apart so there would have to be two-way bus service on each street.
IMO, they should've tried your idea of keeping Olympic and Pico two-way but making Olympic favor westbound traffic and Pico favor eastbound traffic based on the light timing (and perhaps more lanes in the dominant direction and also controls over the left turn signals). Local traffic and buses could still travel in the unfavored direction, but through traffic would know that they could benefit from the timing to move through the city faster. It would work in LA because the traffic is busy, but relatively balanced.
Another possible pair of street to try the timing is Washington and Adams that connect the area just south of Downtown LA to Culver City. The two streets parallel the 10 freeway and could serve as a relief route to the busy freeway. Plus, Adams ends at Washington at the eastern end of Culver City, so conceivably all traffic west of that point could take either street to reach Downtown LA or to an intermediate freeway entrance.
The benefits of a well-timed traffic corridor are amazing. You can often make better time on 1st Ave in NYC than on the parallel FDR Drive.