m1 = ConvexHullMesh@RandomReal[{0, 1}, {10, 3}];
m2 = ConvexHullMesh@RandomReal[{0, 1}, {10, 3}];
intersection = RegionIntersection[m1, m2];

Volume /@ {m1, m2, intersection}

RandomPoint@m1  (*works*)
RandomPoint@m2 (*works*)

RandomPoint@intersection (*returns CompiledFunction errors*)