More openings at higher levels? That's just at odd with how organizational structure works. For engineers, at least, you need about 1 manager per 8 ICs. Going up the ladder, you probably need about the same number per level, so: 8 managers of managers per first level manager, and so on. If you have team managers, directors, and VPs, you should need:
1 VP per
8 directors per
64 team managers.
So, how are there more openings at higher levels?