My experience with computational geometry in Mathematica is that I cannot predict in advance which approach will work for a given problem, and I must be prepared to try something else. I don't ask "why" any more.

It works if you Rationalize the coordinates:

polys = Rationalize@{Polygon[{{0, -2, -2.9}, {0, -1.5, -2.65}, {10, \
-1.5, -2.65}, {10, -2, -2.9}}], 
    Polygon[{{0, -1.5, -2.65}, {0, 0, -2.95}, {10, 
       0, -2.95}, {10, -1.5, -2.65}}], 
    Polygon[{{0, 0, -2.95}, {0, 1.5, -2.5}, {10, 1.5, -2.5}, {10, 
       0, -2.95}}], 
    Polygon[{{0, 1.5, -2.5}, {0, 2, -3.5}, {10, 2, -3.5}, {10, 
       1.5, -2.5}}]};
line = Rationalize@HalfLine[{0, 1, 0}, {1, 0, -.52}];
surface = RegionUnion[polys];
Solve[And[Element[{x, y, z}, line], Element[{x, y, z}, surface]], {x, 
  y, z}]