I think what they will really lose is the perseverance that it takes to write, and various other skills that are made possible by being a skilled writer. They may gain other skills along the way, of course. But it's a big unknown.
However, when you're using ChatGPT to write things for you, you are in a different position. First of all, you're not the audience - you're the editor. This will make your determinations different, as you're re-evaluating a work you're iterating on, and core points of which you're already familiar with. The same applies to writing on your own (where you're both the writer and the editor for yourself), but writing forces you to focus much more on the text and thoughts behind it, which I believe teaches you to make more nuanced determinations, with much greater fidelity.
Secondly, when you're writing - especially if you bother to enlist the help of an LLM - you usually have a specific goal in mind. Writing a love letter, or an advert, or a business e-mail, or a formal request, etc. requires you to think not just in terms of how it "feels" to you in generic sense of entertainment or knowledge transfer value. You need to put some actual thought into the tone, structure and the wording. Writing, again, forces you to do that.
I can get away with letting GPT-4 write half the text in my correspondence at work (INB4 yes, I have temporary access to company-approved model instance on Azure), because I've written such text myself so many times that I know exactly whether or not GPT-4 is doing a good job (I usually end up having it to do two or three variants, and then manually mix sentences or phrases from each). Even with that experience, I still consider it to be a tool for overcoming mental blocks associated with context switching - I wouldn't dare just having it both generate and send e-mails for me. People who never got the experience of writing specialized correspondence, I just don't think they'd be able to tell if the output of an LLM is actually suitable for the goal one wants to achieve.
When I let GPT-4 write text for me (parts of e-mails or documentation), I rely on my own writing skills to rate GPT-4's output. The problem I'm solving isn't "I can't write this". I can. It just requires putting in effort I'd rather avoid, and it's significantly easier to criticize, edit or get inspired from existing text, than to come up with your own from scratch.
People who decide to rely on LLMs instead of learning to write will face many problems, such as not being able to express what the LLM should write, and not being able to quickly evaluate if the output is any good.
Of course, if we keep the current rate of progress, few years from now the world will be so different that it's hard to guess how communication will look like. Like, I can imagine GPT-6 or GPT-10 being able to write perfect text based on contextual awareness and me making a few grunts - but if this becomes ubiquitous, we'll have bots writing texts for other bots to translate back into grunts, and... it's really difficult to tell what happens then.