The growing prevalence of conversational voice interfaces, powered by developments in both speech and language technologies, raises important questions about their influence on human communication. While written communication can signal identity through lexical and stylistic choices, voice-based interactions inherently amplify socioindexical elements - such as accent, intonation, and speech style - which more prominently convey social identity and group affiliation. There is evidence that even passive media such as television is likely to influence the audience's linguistic patterns. Unlike passive media, conversational AI is interactive, creating a more immersive and reciprocal dynamic that holds a greater potential to impact how individuals speak in everyday interactions. Such heightened influence can be expected to arise from phenomena such as acoustic-prosodic entrainment and linguistic accommodation, which occur naturally during interaction and enable users to adapt their speech patterns in response to the system. While this phenomenon is still emerging, its potential societal impact could provide organisations, movements, and brands with a subtle yet powerful avenue for shaping and controlling public perception and social identity. We argue that the socioindexical influence of AI-generated speech warrants attention and should become a focus of interdisciplinary research, leveraging new and existing methodologies and technologies to better understand its implications.