In this position paper, we explore standard language ideology in language generated by large language models (LLMs). First, we outline how standard language ideology is reflected and reinforced in LLMs. We then present a taxonomy of open problems regarding standard language ideology in AI-generated language with implications for minoritized language communities. We introduce the concept of standard AI-generated language ideology, the process by which AI-generated language regards Standard American English (SAE) as a linguistic default and reinforces a linguistic bias that SAE is the most "appropriate" language. Finally, we discuss tensions that remain, including reflecting on what desirable system behavior looks like, as well as advantages and drawbacks of generative AI tools imitating--or often not--different English language varieties. Throughout, we discuss standard language ideology as a manifestation of existing global power structures in and through AI-generated language before ending with questions to move towards alternative, more emancipatory digital futures.