I am intrigued by this and if true I am surprised that I didn't see it mentioned before.
I don't know if it is OK for me to invoke
@Bagpacker given that we were arguing in another thread today, but he has given a lot of detailed info about Swiss taxes before so let's see if he if I can get his attention...
No problem with arguing - that's the nature of this board.
Regarding the Japanese crypto trader and her 0.05%: For a professional trader capital gains are not tax free. In fact, the Japanese is even responsible to pay AHV (social contribution, so-called "first pillar") on it. No matter in which canton she resides, her overall tax rate would be significantly higher than 0.05%. These 0.05% hardly cover Swiss wealth taxes which are due after your fortune crosses a certain threshold (-> >100k , depending on canton and village).
Even if she considers herself as not being a "professional" trader and she would wrongly assume to be a "private" investor, her capital gains from crypto investment are not tax free because they are (most likely) her main source of income.
The above is called "ordentliche Besteuerung" (ordinary taxation).
Note: Capital gains are only tax free when these do not make up for most of your income.
However, this person is a Japanese. Depending on the canton where she lives, it can be that she struck a deal with the tax office of her canton and pays a "lump sum tax" (Pauschalbesteuerung).
It is a bit similar to what Italy has on the cheaper site (in Switzerland you will not get that deal for the Italian "fee" of EUR 100k).
Such "Pauschalbesteuerung" would require her to only trade outside of Switzerland on assets who are not related to Switzerland.
Lump sum taxation ("Pauschalbesteuerung") is only available to foreigners (i.e. a citizen of Switzerland will never be able to get such a deal) and it is only offered by a limited number of cantons (for instance the canton of Zürich abolished it a few years ago). The matter of lump sum taxation is highly political. Ever more cantons are abandoning it. Nevertheless, if she has millions of trading income this would be the only solution for her to legally pay 0.05%.
Please note: Lump taxation for a professional crypto trader would be a novum. In today's political environment it is rarely granted and if granted than this status is preferably given to foreign celebrities.