I believe LX obtained the rights to Swissair from their executors but have not (yet) decided to use them, perhaps for the reasons you state.
However I've noted that many people here use Swiss Air, when referring to LX. It's easier to say than Swiss International and is less confusing that just saying Swiss.
When they were created they used the name for the country in all four national languages plus English. Now we only see the English version. (But this is a bit of a thread drift)