Swiss accounts can be opened for smaller values – but if you do not have a minimum deposit level of around 7,500 Swiss FRancs (CHF) then you’ll be charged monthly fees of about 2 CHF.
It is a realistic way to do business – and only the most draconian of governments would prevent their citizens from holding one.
Be warned though that Swiss banks will charge more than US banks for basic day to day dealings – and international posting of statements will mean a higher running cost.
Also if you run a credit card with you’ll be hit with “currency conversion fees” on everything that is not is your base currency – so the costs can add up – but it’s not excessive. Perhaps $80-$100 pa in charges.