Why can't woodwind players change key through mouthpieces and head joints?

With brass instruments that use crooks to change key, the only way to play different notes is to go up and down the harmonic series. If valves are involved and a longer crook is used, the tuning slides on each of the valves has to be adjusted to compensate for the difference in tube length. Otherwise, they would be out of proportion with each other and, therefore, out of tune.

With woodwind instruments this compensation isn't possible; the vent holes being placed specifically where they need to be for the pitch of the instrument. Alter the tube length and the vents become in the WRONG places, making the fingered notes out of tune.

Its because where the holes are located have to be in the ratio to the length of the instrument. So if you put an extra long mouthpiece on a Bb clarinet it would play very out of tune because the distance between the finger holes would be in the incorrect ration to the length of the instrument

Because the distance between the keys is constant. Making the barrel longer, will change the intonation of the instrument.

Those were all good answers.

Del Man, thank you for answering the question,

and without commenting on how stupid the question was!