The disappearance of the joystick
Solution 1:
why did the gamepad take over from the joystick?
Many reasons!
My tuppenceworth: I guess once the NES pad came out, people making gaming hardware just copied it.
Firstly, from a business point of view, it has less plastic in it than an old style 8-way joystick, and offers the same precision of movement. Gamepads are significantly more compact and less bulky to store than old school joysticks too. Cheaper to make, smaller, better for business.
Personally, I think the main reason is one of optimal interaction within the constraints of the product - you don't need to rest it on a table, it takes up next to no space, and it can be more or less covered in controls as long as the user can reach and use them all comfortably.
IMHO gamepads represent an evolution of the old school joystick, (where the fitness function includes cost, ergonomics, and functionality available at your fingertips) and so they've naturally taken over from joysticks.
Sure it's less buttons than you'd need for a PC flight sim (every button on the keyboard anyone?), but you just don't need that many buttons for the vast majority of games.
TBH, the thumbsticks on an X360 pad offer the same angular resolution as any typical flight stick; so the only real reason for the massive flight stick still existing is that players want to have a joystick that makes the experience feel as close to how they imagine the real thing as possible - certainly that's why I bought one of those massive flight yoke things with the throttle controls and about a billion hat-switches to play Apache Gunship in 2001 :)
Solution 2:
This really depends what you're playing - platform and game style. I doubt we'll ever see, or really want, a full-size joystick for console gaming. However, the joystick is alive and well for PC games, where it is used for everything from FPS to flight simulation. On that platform, its advantages are that it is more precise than a gamepad and supports more axes than a gamepad. On the other hand, it is primarily a one-hand control vs. the gamepad that is operated with both hands. On a PC this makes sense since you would often have keyboard commands or a throttle control as well. On a gamepad, all of the controls are right in front of your fingers. It's a trade-off of convenience vs. simplicity, since only a small set of commands can be represented.
Solution 3:
Well actually for the gamepad you only need your thumb to steer, which gives you a better reaction time.
With a joystick you have to move your hand much further to get to the opposite direction, which is in fast games relevant. Plus: This actually makes you to afford more power than necessary, so that Joysticks have to be built much more robust.
Just my two cents