I've been trying to use an enum as the Discriminator type, but than I get this error:

<enum> is not a valid discriminator type.

Anybody know why this makes sense?

Because discriminator values aren't visible to the object side of the architecture. What the database knows as the discriminator value is translated to the object side as the class of the object. It doesn't make sense to define the discriminator as an enum, because there would be no use for it. So, going to the trouble of translating a string in the mapping to the associated enum value then numeric value for the DB was probably just left out.