If we're talking about the public good -- rather than the very narrow interest of Pyramid and a couple Salina landholders who want a high-speed freeway connection to run uninterrupted past their properties -- I can't think of any problems that a tunnel would solve. Onondaga County has a parallel, higher-speed freeway to the east, and it doesn't have any traffic to speak of.
And downtown Syracuse and adjacent neighborhoods aren't lacking for green space - far from it, they're only suffering from a lack of density. The real estate values along the corridor are depressed because of the traffic volume and the built environment. While I'm sure some projections for community improvement are pie-in-the-sky, the idea that the grid solution is singularly able to improve the corridor is perfectly reasonable. This chart can better illustrate what I mean.
View attachment 153976
The highest-value real estate in the county flanks the Almond Street corridor on both sides. It plummets in the area where the character of the neighborhood suffers because of the viaduct.
A tunnel could theoretically solve this: a deep bore tunnel could enter the ground around East Colvin Street and emerge near the mall. The Almond Street corridor could support hundreds of millions of dollars of new development. But we wouldn't be getting much utility from that tunnel, because it wouldn't offer direct access to downtown or the hill, and it wouldn't connect to 690. Further, because it would certain be tolled, a lot of traffic would shift to the existing grid anyhow.
To answer your Princeton question, I always take 206 through town and don't know of any parallel through streets. It's slow sometimes. In Syracuse, 88% of the traffic on the viaduct has a destination or origin between the two 481 termini. A big percentage of this is bound for downtown or the hill. That is, they're all using the grid already! Congestion results from the chokepoints on and approaching the interstates. The essence of the grid is that there are dozens of redundant streets - motorists would leave the freeway and disperse onto city streets that provide more direct access to destinations (and are running over 90% below capacity at all times).
Hope that answers a couple questions.