Would not it be useful to have the angle of attack information displayed on the flight display? I know that we have shakers that alert pilot when the critical AOA is exceeded, but still we have cases of pilots stalling the aircraft (sometimes stalling one wing more than other). I am sure designers have considered this but not chose to display AOA. I am curious what the reason could be.
Many aircraft do include them, because it's very useful.
For example a modern 737:
A Garmin G1000 (one of the more common General Aviation glass cockpits):
Specifically the part that looks a bit like this
And a more traditional analog/mechanical gauge:
The problem is that usually when someone stalls, it's because they've made a mistake - not because they can't see the AoA. Either they're disorientated, or they've made a mistake with airspeed or an obstacle and are exceeding the aircraft's performance envelope.
Typically, the lack of an AoA dial isn't the reason you stall.
Slightly off-topic, but I recently came across the "side string" which gives a direct reading of AoA. Every gilder pilot is familiar with the yaw string, but in two years of learning to fly gliders, I'd never heard anyone mention the side string.
Now, in the ultralight / open-cockpit world they use a single piece of yarn mounted on a stick, which acts as a combination yaw and side string.
It strongly depends on the aircraft we're talking about. As an example, this is the Head Up Display of an F/A-18 "Hornet":
The number near the α is the angle of attack (AoA or α) measured in degrees.
I presume that only in certain conditions knowing the exact value of the AoA may turn out to be useful (when nearing the limits maybe...). Usually, exceeding the maximum AoA is a the result of a mistake, not the mistake itself.
Fly-By-Wire systems usually do not allow the pilots to exceed the max AoA (Airbuses' Alpha Floor for instance) during normal operations.
As others have noted many aircraft do have AOA indicators. Military A/C tend to have them next to the HUD on the left side.
The advantage using AOA over stall speed is that the stall AOA is constant while the stall speed depends upon weight. Greater weights => lower stall speeds.
This difference will be important when there are large differences in A/C weights. If your F-18 has 4x2000lb bombs the stall speed is much different depending upon whether those bombs are dropped or not.
With your average cessna, the weight change of the A/C/ does not change the stall speed significantly. An AOA indicator does not provide as much value relative to its cost and weight.