I feel like for most emails I write, information density is close to a maximum. This means there's no actual gain to be had from a language model. The email I would write myself is going to be about the same length as the prompt I'd have to write anyway.
Even if English is your mother tongue, if your written English is crappy or you need to write in a style you are unfamiliar with (e.g. formal), then ChatGPT can help.
I also think writing yourself might be far better practice. This tool can easily become a crutch. This is unlikely to be free anytime soon. In fact it's likely to be quite expensive.
I can ask ChatGPT to rewrite an email in the style an American news reporter from 1950, and I can judge whether some of the cliches it generates feel correct. I cannot write in that style at all.
Whatever LLM search stuff comes along will only be free as long as it brings in ad revenue. Which involves making the models fundamentally worse most likely. Or they'll use it to collect personal data. Probably both.
Computationally, GPT is wildly expensive. This idea people have that it's gonna be used all over the place for all sorts of tiny tasks, as if it's just another REST API, is nuts. Unless something fundamentally new comes along that makes these models much cheaper, adoption is likely going to end up much more limited than people expect. Or siloed off into expensive business-facing products.
If I'm making (or valuing my free time at) $20 an hour, then ChatGPT only needs to save me one or two seconds and half a minute respectively.