[1] (and because Pb63Sn37 or the inexplicably more popular Pb60Sn40 are eutectic and near-eutectic, respectively, which is nice for wire dipping and related sports)
The reliability problem could be solved only by replacing soldering with another method of making electrical connections during PCB assembly, e.g. thermal/ultrasonic welding of copper on copper, metal deposition in vacuum etc.
While replacing soldering is possible, any known alternative method would hugely increase the price for the assembly of electronic equipment.
Soldering is not used because it is a good method for making electrical connections, but because it is extremely cheap, allowing many thousands of connections to be made simultaneously, during a pass of a PCB through a reflow oven, or over a soldering wave.
There's been some interest in laser welding for PCB assembly. But most modern components are not designed with the pins out where you can get at them with a laser beam. Laser welding is commonly used to weld the connections in automotive battery packs, so it does work.
The whiskers are not related to soldering. Of course there are some soldering issues which facilitate whiskers but that's about it. Tin is a normal plating material so you can find whiskets in places which were not soldered.
