Wondering hit the nail on the head.
Higher alt = thinner air, but
Higher alt = colder air too.
As altitude increases and air density decreases, thrust reduces.
As altitude increases, temperature reduces, offsetting some of the effect this density decrease has on thrust produced.
Rate of climb is dependant on excess thrust available (that over and above the amount required for straight and level flight). Since ~FL370 is theoretically where the tropopause is, jets find that lavel their theoretical optimum, since climing higher results in thinner air with no offsetting temp decrease. As a result, excess thrust diminishes above the tropopause. Unless the aircraft has buckets of excess thrust, (ie concorde)and is more efficient AND still aerodynamically stable in the thinner air above the tropopause where aerodynamic damping is also reduced, the amount of excess grunt required to get higher, and the amount of stability augmentation required to keep you upright negate the cost benefits of reduced drag and fuel flows.
That's what I reckon.