Why don't planes use pulsejets? According to my research, a pulsejet's thrust grows as the airspeed increases. Most pulsejets require no moving parts which makes it easier to manufacture them. They are also very lightweight which can have some great effects on aircraft.

They are very slow at zero airspeed but very fast at high airspeeds. Therefore you could simply have a normal jet engine to power the take off and then switch after take off to the pulsejets.

Here is an example where I've labelled a DC-10 of what a pulsejet with jet engine plane could look like:



The plane would taxi onto the runway using the jet engine as power, it'd then line up on the runway. It'd then power its jet engine and take off. Shortly after take off it would switch to the pulse engines and optionally turn the jet engine off.

So why don't planes use pulsejets? Surely they would allow planes to go faster and in turn allow them to reach destinations quicker. Also the pulsejets are easier and cheaper to produce than jet engines and there lighter than jet engines.
2 reasons really:


Airplanes need most of their thrust right when their airspeed is low. (to get more airspeed at takeoff and go-around). 
The maximum airspeed in cruise is not dictated by how much thrust the engines can throw out. Instead it's dictated by the aerodynamic forces on the airframe. They cruise right below the speed of sound where the rules of aerodynamics change drastically. Going too fast would rip an airplane apart.