Why aren't there any jets with horizontal-stabilizer-mounted engines?
There are two configurations I can think of.
1. The jet mounted on the horizontal stabilizer (above, below, or the tip)
Unlike the vertical stabilizer, the horizontal stabilizer is trimmable (THS). It's constantly moving, which means when it moves, so would the thrust line. A kind of thrust vectoring that you don't want. For example, trimming for slow flight during approach, the thrust line will point down and aft of the CG, which will in turn point the nose further up, this is a kind of a destabilizer. Even if the angle is not too big, the changing thrust line will always act against the intended trim. And lastly with the engine constantly on the move, the blade tip clearances will need be bigger, which will in turn reduce the engine's efficiency.
The required strength issues that result in a heavier weight are also a factor. This also impacts the loading flexibility; a tail heavy plane will reach a point where you can't put as many passengers in the back without adding a forward ballast.
2. The jet mounted at the root and doesn't move with the THS
While certainly achievable, like the L-1011's number two engine wrt the vertical stabilizer, the issue here is not why aren't the jet engines there, it's why the THS is not there.
The horizontal stabilizer of a plane like the DC-9 (and its extended family) is purposefully placed above the tail, creating a T-tail. With the tail swept back, the top of it is farther from the plane's center of gravity, giving the THS a bigger moment arm, and in turn allowing a smaller THS, and the other benefit that comes out of that is the end-plate effect of the T-tail, which also permits a shorter fin for the same control authority.
You'll also notice buried engines are of the older small-diameter type, except for large planes like the L-1011, but still that makes maintenance access a lot harder, than an exposed engine.