Large language models are increasingly being integrated into applications that shape the production and discovery of societal knowledge such as search, online education, and travel planning. As a result, language models will shape how people learn about, perceive and interact with global cultures making it important to consider whose knowledge systems and perspectives are represented in models. Recognizing this importance, increasingly work in Machine Learning and NLP has focused on evaluating gaps in global cultural representational distribution within outputs. However, more work is needed on developing benchmarks for cross-cultural impacts of language models that stem from a nuanced sociologically-aware conceptualization of cultural impact or harm. We join this line of work arguing for the need of metricizable evaluations of language technologies that interrogate and account for historical power inequities and differential impacts of representation on global cultures, particularly for cultures already under-represented in the digital corpora. We look at two concepts of erasure: omission: where cultures are not represented at all and simplification i.e. when cultural complexity is erased by presenting one-dimensional views of a rich culture. The former focuses on whether something is represented, and the latter on how it is represented. We focus our analysis on two task contexts with the potential to influence global cultural production. First, we probe representations that a language model produces about different places around the world when asked to describe these contexts. Second, we analyze the cultures represented in the travel recommendations produced by a set of language model applications. Our study shows ways in which the NLP community and application developers can begin to operationalize complex socio-cultural considerations into standard evaluations and benchmarks.