The only time I have ever heard of an inspector even talking about a bathroom floor is if there is another dwelling below you (basement apartment being rented out). There are no codes or laws for a normal one family dwelling. I am sure certain towns may have something for apartment buildings and such but the answer is no.
Should you use one? Seriously debatable. If you have a shower open to your entire bathroom or if what is below your bathroom is worth a lot then yes. So for example if under you bathroom was you 100K kitchen... then yes. But these systems are too expensive and laborious for your average bathroom. Do you really expect someone to pay an extra $500 for a membrane in a small bathroom?
However tile plus baseboard plus caulking under baseboard can hold a lot of water.