My standard swiss banks always offered me to ship the replacement cards to anywhere in the world as long as I notify them how long I am in which country. I see no reason except cost-saving that an online bank shouldn‘t offer it.
However you need to be a resident to open an account, and at the very least keep a permanent address in Switzerland if you travel for extended period of times unless you're ready to pay outrageous fees as a non-resident. So this doesn't really answer OP's question.
Incorrect. You can open accounts as a non-resident. However if you're afflicted with USA citizenship they'll generally tell you to get lost unless you have a lot of money.
You will have to pay fees, correct, that's just the cost of compliance in today's world though. The fees are comparable to fees at US based banks FWIW (except the US banks will charge those even to residents in certain cases).