It's not hard to just move your savings. A lot of people do that actually; just keep the standard banking account for daily payments and all other services, and put savings in bank-managed ETFs, time deposits, or savings accounts with other banks (I do all three).
It's not hard to move your savings but due to some "coincidence" all Dutch banks keep their interest rates within a very narrow band (some advertise with higher interest rates you get for 6 months). Dutch people are very averse to banks outside of the country due to the icesave affair and not trusting that for example Estonia or Italy will actually be able to make them whole in case of a crisis. So in the end are you moving your money from Rabobank to Andolubank (whoever they are) for 0.3% more interest? Probably not.