Relation between vertices, cells, and vertex-cell-incidences in 3D subdivisions
Doesn't $F + V \le 2I$ hold trivially for every system of incidences between things called vertices and things called faces? Under some reasonable assumptions, every vertex has at least one incidence, and every face has at least one incidence. If you add those incidences together you count each incidence at most twice.

To get from there to your desired $F + V \le I/2 + O(1)$ you'd need to use some actual geometry show that the vertices and faces each have at least four incidences on average. This is obvious for convex subdivisions but maybe needs more assumptions in general (e.g. consider a system of bubbles in 3d space, linked one to the next in a chain: each face has no vertex-face incidences, because there are no vertices).