I'll accept the intuition, but culture seems even harder to quantify than individual welfare -- and the latter isn't exactly easy. I'm not sure what we should be summing over even in principle to arrive at a function for cultural utility, and I'm definitely not sure if it's separable from individual welfare.

One approach might be to treat cultural artifacts as fractions of identity, an encoding of their creators' thoughts waiting to be run on new hardware. Individually they'd probably have to be considered subsapient (it's hard to imagine any transformation that could produce a thinking being when applied to Lord of the Rings), but they do have the unique quality of being transmissible. That seems to imply a complicated value function based partly on population: a populous world containing Lord of the Rings without its author is probably enriched more than one containing a counterfactual J.R.R. Tolkien that never published a word. I'm not convinced that this added value need be positive, either: consider a world containing one of H.P. Lovecraft's imagined pieces of sanity-destroying literature. Or your own least favorite piece of real-life media, if you're feeling cheeky.