I understand why passenger jets use software that overrides pilot inputs that might cause the jet to exceed the flight envelope. But why do passenger jet manufacturers design their planes with stall prevention systems? Shouldn't professional pilots be well aware that a stall is possible when the airspeed is too low, or the angle of attack is too high?
Why do car manufacturers install seat belts? Shouldn't licensed drivers be well aware that they should slow down when it's raining or snowing and that they shouldn't run through red lights or stop signs?
A better analogy:
Why do car manufacturers install anti-lock break systems? Shouldn't drivers know that when their brakes lock up they should release brake pressure and/or pump the brakes quickly to slow the car down?*
*To be fair, I don't think this is actually taught in driver's education (at least in the US) anymore - my kids learned this from me, but never reported being taught and/or practicing when they took driver's ed. One of the many reasons flying is safer than driving.
To be certifiable, airplanes have to have some kind of cues to warn when you are getting close to a stall, and have decent behaviour during the stall, because nobody is perfect. Airplanes with very strong physical cues prior to stall, like the whole airframe shaking, and good behaviour during a stall, like a good natural pitch over tendency with immediate unstalling of the wing, can get away without stall warning and prevention systems.
Transport aircraft with highly loaded wings and high performance airfoils may have poor behaviour before the stall (no buffeting or shaking), and poor recovery performance after, and need a little help. The airfoils used for airplanes that fly at near trans-sonic speeds tend to suffer from this because they tend to stall from the leading edge, at which point the wing stops lifting all at once, and there is often no prior buffeting or shaking.
The earlier supercritical (higher critical mach#) airfoils developed in the 70s were especially bad for this because they developed a flow separation bubble just aft of the leading edge at high angles of attack, due to the profile that was used to manage the formation of shock waves (the Challenger business jet and CRJ200 Regional Jet is typical). You do not want to experience the natural stall on such an aircraft and some kind of system has to be in place as a backup for mishandling of the airplane by the pilot.
For airplanes with mechanical/hydraulic controls, to provide a tactile warning as a substitute or supplement for the airplane shaking (pre-stall buffet), stick shakers are used, which is just a motor with an eccentric weight on the control column. If the post stall behaviour (not much natural pitch over, or worse, settling into an unrecoverable deep stall) is poor, a stick pusher is installed to give the control column a shove just before the natural stall occurs. The stall protection system calculates when to do all this.
Most high performance aircraft use shakers, and some use stick pushers. With FBW, the FBW computers intervene directly within the control loop to achieve the same end without having to shake or push the controls.
You said you understand systems to prevent the airplane from exceeding the flight envelope. Stall is just another boundary of the flight envelope. The rest of the envelope limitations are listed in the flight manual as well. Shouldn't pilots know not to stall the airplane, just as they know not to over-stress it, or exceed other limitations? Of course.
But humans make mistakes, they can get distracted or disoriented. And just as there's little benefit to allowing a pilot to rip the wings off the plane by pitching too fast, there's little benefit from allowing the plane to stall.
Here is a selection of aircraft that have crashed due to stalls.
Thai Airways International flight 261
If stall protection systems are implemented and functioning properly, they can prevent issues. Here are just a few instances where stall protection worked as intended:
The relevant certification requirements, set by the FAA/JAA/CAA etc require that a "large aircraft" that is capable of stalling has an automatic stall warning and recovery system. So the simple answer is "because the rule of law says so".
Maybe you could think about re-phrasing the question to ask why the traditional stick shaker and pusher, with a long and satisfactory history, were not used? I expect that Boeing will be having to answer that question to the authorities.
Well, stall is a limit to flight envelope, the one exceeding which is most dangerous, so stall prevention system is one of the systems that override pilot input if it would lead to exceeding the flight envelope.
And note that stall is directly related to pilot input, because in stable aircraft¹ the angle of attack is directly controlled by elevator and stabilizer position² and stall occurs when the critical for given configuration is exceeded.
¹ All transport aircraft are longitudinally stable. Only unstable aircraft are some new fighters (and some very early experiments).
² The stability makes the aircraft always pitch so as to assume the “trimmed” angle of attack determined by the control surface position. It is a first order feedback, so no oscillations, and it takes really abrupt control input, or severe turbulence, to create a significant momentary deviation.