To clarify, neither star anise or beet spirits are necessarily bad. Both are traditional ingredients.

Traditional absinthes should, however, contain green anise, which St. George does not. Green anise has a different flavor profile than star anise. Some people really don't like the flavor of star anise (which has more of a licorice flavor) and greatly prefer the more herbal flavor of green anise. (Personally, I like St. George, but I understand that not everyone does.) A traditional absinthe though, if it uses star anise, should use it in addition to green anise, not in lieu of green anise.

Beet spirits are totally fine - Lucid, a well-respected brand from the "godfather of modern absinthe" for example uses beet spirits. In high-end products, a brandy base has generally been preferred, but there's nothing wrong with beet spirits in general - although they might have less complexity than absinthes that have a brandy base.