You will likely enjoy the right blackberries which are few and far between. My heirloom blackberries have a nice flavor. Like any fruit there are plenty that have that bitter after taste that some people such as @scottfsmith can easily detect as well. Scott I recall grew a variety that he was going to remove for the reasons you mentioned of the bitterness. Those blackberries he does not care for is likely Because of the high level of salicylic acid they contain which has the taste of aspirin. Certain soils seem to bring it out more than others. This link I think you might find interesting
Berry Health Benefits Network | College of Agricultural Sciences . Blackberries are very healthy and delicious but a friend mentioned to me the first of the series which I think is prime gem were not desirable flavored in his opinion but advised he was told both prime ark freedom and prime ark 45 had a nicer flavor. I’m growing them to extend my crop but when it comes to flavor time will tell. It’s hard to beat the flavor of the blackberries I already have. The blackberries I’ve had from the store did not taste good at all. Part of taste is location and in Kansas like Texas the sun is very hot which really improves blackberries flavor. In the case of some blackberries they are just far to tart to be good. A good blackberry is sweet and delicious with no bitter aftertaste and no tartness at all. I have a variant of my heirloom berries raised from seed that have a bitter aftertaste but it’s not intolerable but not as good as my main 2 acres taste. See this post since several varieties are discussed Blackberries by the gallons