Okay, so here's what's what. Tin whiskers have been known for ~100 years. Originally solder was just tin. Lead was added specifically in the 30s or so to avoid tin whiskers [1] though nobody knows why that works. RoHS/lead-free has been around for ~20 years and there hasn't been a definitive solution.
[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)
It is extremely unlikely to ever find any solution to the tin whiskers problem, other than alloying tin with toxic elements, i.e. either lead or antimony.
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.
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.
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.
If you can get the parts you need in SSOP or TSSOP packaging, with the pins visible from straight down, laser brazing might work.
Brazing is done at higher temperatures than soldering, but with a laser, you can apply the heat to just the area of interest, and hopefully not cook the ICs. Laser soldering already exists, and there are laser cutters, so adapting one for laser brazing ought to be possible.
The advantage of brazing is that you can use many more materials, most of which don't contain either tin or lead. Low-cost aluminum brazing rod or wire might work. Working temp around 700C. This is going to take careful heat management. Worth a try for aerospace applications.
> 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.
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.
The only reason for using tin is soldering. Tin is used because it is the only metal with the right melting temperature, neither too low nor too high.
When you do not use soldering, you do not need tin. While it is possible for whiskers to also form on other metals, the chances of this happening are negligible in comparison with tin.
So yes, the only reason for whiskers being a serious problem is the need to use soldering.
[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)