The explanation is probably that healthy liver cells are very expensive and annoying to grow (they need to come from a biopsy and stop dividing quite fast), whereas cancer cells are cheap and easy (they never stop dividing, i.e. they have cancer), so for researchers it is far easier to work with cancer/"immortalized" cell lines.
Regarding the anticancer effect of flavokavains, I must admit that I am not too optimistic. Their mode of action is most likely inhibition of glycolysis by alkylation of some of the key enzymes, which in turn leads to apoptosis. This is a fairly well-known mechanism, see e.g.
https://en.wikipedia.org/wiki/Iodoacetic_acid#Possible_cancer_therapy
If this is indeed the mechanism, it would explain the general toxicity as well as the anticancer effect (cancer cells are often more glycolytic and thus more sensitive to these alkylators).