> Are you sure? TSMC definitely does packaging. And it seems like it would be crazy to ship a delicate unpackaged die to a different factory when you could just keep it in a clean room and do everything in one place. I think it would be mad for Intel not to do packaging there.
True, the very advanced packaging techniques, such as TSMC CoWoS or Intel EMIB, are done at the fabs by those companies. These packages are for very high performance multi-chip interconnects. In both cases, the "package" itself actually is partially constructed from silicon, so we are kind of blurring the lines between what is "chip" and what is "package". The vast majority of chips do not use packages anywhere near this advanced and are not done at fabs.
Also, it's not crazy to ship finished wafers (i.e. "unpackaged die"); it's standard practice. Once the final process steps are complete in the fab, the chip is not as sensitive to fine particles any more. The wafers get loaded into cassettes then vacuum-sealed in anti-static bags. They ship out to the backend assembly sites just fine. In fact, globally, there are probably ~100,000 wafers shipped like this every day.
> Intel sells lots of CPUs that aren't soldered to PCBs.
True. But if you are buying an LGA socketed Intel CPU, the silicon die had to first be mounted on a substrate and the heatspreader attached. That wasn't done at fab, it was done at backend assembly. Ever notice that Intel CPU's often say something about "assembled in Malaysia" on top? That's because it was assembled in Malaysia. Intel does not have any semiconductor fabs in Malaysia, meaning, they fabbed it in one place and assembled it in another.
If you are a company like Dell or HP and you are buying the laptop BGA CPUs, Intel still had to assemble those into the BGA package before shipping to Dell/HP. And the BGA package assembly also is not done at fab.