Is there a reason that nobody is doing this?: If making your flash drive hidden but accessible was a goal, something like this would be perfect. This is a 128gb drive by SanDisk and runs Wii games in wbfs format just fine. It was only 20$, and since the Wii won't use the drive at 100% constantly (unlike running Windows on this), the drive should stay cool. What are the real downsides to removing it from it's metal casing other than heat dissipation, as I'm sure the other slim drives used in portables have something similar sized inside.
Some drives die very easily when you solder wires to them. I am sure both me and @JacksonS killed a Samsung Flash Drive FIT by doing that. Maybe with a low melting point alloy like Sn42/Bi58 you can avoid this issue.
If that's the same one I used it also heats up immensely as long as it's powered. Samsung FIT is good though.
Yeah, I run Windows on this and aside from the fact that I do not get anywhere near the advertised speeds (and horrid >100 ms response times), it does tend to get very hot. I use a different drive for the Wii, as that one has less storage space and runs cooler.