Is anybody killing each other and destabilizing the world over those other religious places?
Houses of worship can be built anywhere. This is not one of those. The Mount is the ruins of the foundation of a building, and because a bunch of people think it's magical they've slaughtered each other over multiple millenia. Obliterating it would be a mercy to them.
From a theological perspective, it is impossible to obliterate the site. The site is not important to either religion because of a building, or a wall or a ruin or a foundation. The site is holy to Jews because it is the one place on earth where the Shechinah (the spirit of G-d) rests. The site is holy to Muslims because it is the place where Mohammed ascended to heaven. You can blow a hole into the place the size of Manhattan and it would still be these things.
You have to ask yourself, instead, WHY this is such a place of contention.