The simplest example would be speech recognition. With the exception of Keyword Spotting Systems like Hey Siri or OK Google, it's currently practically impossible to implement larger vocabulary speech recognition on device.
Google will happily permit you to download trained models of <100MB to your phone via Google Translate, which permit not only offline vocabulary recognition of a remarkably wide range, but will also then translate that input into another language (also offline).
I believe the restrictions imposed by keyword-spotting have more to do with the always-listening and/or power-efficient nature of the task, rather than the restrictions on the legibility of offline speech recognition.
I'm pretty sure larger vocabulary local speech recognition on devices with less computing power than modern smartphones has existed (products for continuous speech recognition on PC go back to at least Dragon Naturally Speaking in 1997.)
I believe the restrictions imposed by keyword-spotting have more to do with the always-listening and/or power-efficient nature of the task, rather than the restrictions on the legibility of offline speech recognition.