I'm not convinced..
Washington Street and Watertown Street are different kinds of road. Washington Street through Newton Corner, Newtonville and West Newton primarily serves businesses and multi-family residences, whereas Watertown Street through Newtonville and West Newton is almost entirely small-scale residential. Washington Street carries a lot of longer-distance travelers getting on and off the Turnpike whereas Watertown Street does not.
In the Federal Highway Administration functional classification, Washington Street would probably be considered a major collector and Watertown Street a minor collector, but the road-narrowing project may turn Washington Street into a minor collector as well.
When the Washington Street changes were being first discussed, I expressed concern that the traffic impediments being proposed would push non-local traffic onto Watertown Street and other more-or-less parallel roads. I don't think I was the only one to talk about this, and as result was told that traffic on Watertown Street would be monitored to support a before-and-after analysis. It's not just traffic counts, though. My informal observation is that in addition to more cars, more heavy vehicles, not necessarily making local deliveries, are using Watertown Street probably because it's faster. Unlike Washington Street, Watertown Street has few traffic controls - great for drivers who want to move faster than Washington Street would allow, not so great for people in the neighborhood who need to pull out of a side street onto Watertown Street.
Many people using either of those two streets would have to make a loop to change direction, adding even more traffic. Even without that, try to think about what 100% of Washington Street traffic, in one direction or the other, would do to Watertown Street.
A lot of the motivation for the Washington Street work was, as I recall, to make it easier and safer for cyclists, including Newton North students. This proposal would force many cyclists to traverse two busy roads.