Please forgive the interruption, but "most places have a double-taxation agreement so there is no more to pay" depends on the tax rates. If you are paying 40% tax and tax at home is 30%, there is no more to pay, but if you are paying 30% and tax at home is 40%, you owe 10%. Tax residency is usually clearly defined by home legislation. All double-taxation treaties do is ensure you don't pay 70%, they don't allow you to pay nothing or the lower tax rates as suits (many double taxation treaties now mention ships crew and aircraft crew specifically). It would be unwise for employers to leave tax payment up to the individual, because, for example, UK legislation allows Revenue to go straight after the employer in the case of non-payment of taxes. Of course, the taxman may never catch up with you, but increasingly in Europe it is tightening up, plus the taxman's interest in some pilots who think that tax laws don't apply to them.
Incidentally, having the facility to switch currency is extremely unusual, and something to be taken advantage of if it does.