Actually the Tappan Zee was built where it was because engineering-wise, it was an ideal spot. Though the Hudson is about its widest point in that area, the waters are comparatively shallower making the bridge easier to build. The new Tappan Zee is already well under construction and the progress being made is incredible. I’m thinking they are afraid the old one might fail at any minute.
If you see footage of the Tacoma Narrows bridge swaying before it fell, and bear in mind the wind advisories they have for the Tappan Zee bridge, then its placement is foolish. If NY was willing to share revenues, the bridge should have been built further south (where the river is more narrow).