arcgis desktop - Determining if point is surrounded using raster processing

I am attempting to improve a currently extremely cumbersome vector/python process for a natural hazard model. At the moment we have a lengthy script which generates distance/bearing lines from a given point to determine:

1. the type of polygon that it intersects (e.g.. Forest, grass, swamp, etc)


2. the distance to that polygon


3. how many of these lines intersect polygons, to determine how 'surrounded' it is.

There's a lot more involved but that's the gist of it. I am trying to find a way to improve this and am currently stumped on part 3. The idea is to determine if a point is completely surrounded by polygons, within say 200m

So in my attached image, I would want point A to be marked as being at higher risk than point B as it is completely surrounded by my polygons. This is repeated for about 13 million points so is not a small task and I would rather have a surface to derive values from, rather than running our script. I'm thinking there's got to be a variation of hydrology tools or cost-path to do this but I can't seem to get my head around it.

How could I go about this?