Yes, Visvanath, I completely agree with all the points you've made!
Re: the "improve my writing" part, without going into the nitty-gritty of "interlanguage development" I think it's easier to think of this kind of explicit form-focused corrective feedback as like going to physiotherapist, i.e. one session isn't going to change how you use a particular word, phrase, or language pattern ("item" from now on). All of us have built up experience over any number of encounters with that item & with each encounter it becomes strengthened & more entrenched in long-term memory (this is now an uncontroversial principle in first & second language acquisition research). In order to change how we use a particular item, we need to train ourselves over a period of time over multiple sessions. The difficult part is which techniques & strategies work best to make that change in a way that transfers to instances when we speak &/or write. Most traditional "grammarian" methods don't transfer which is another reason why typical interventions with corrective feedback tend not to work very well (what we'd call a lack of "transfer appropriate processing").
So, working with a human or machine assistant while we write, providing corrections, suggestions, etc., however well-intentioned, does little to nothing to help out interlanguage development. The encounters are too infrequent & do not require us to process the corrections & suggestions in a way that leads to longer-term learning.
In case you're thinking, like many others, "Ah! All learners need to do it have the corrective feedback explicitly presented to them so that they can attend to them later." which is very easy to do with interactive chat logs, ...well, that tends not to work very well either. This kind of feedback works well in the feedback session but, as commented above, tends not to lead to changes in how items are used in real world speaking & writing. I wrote a blog post about this here: https://matbury.com/wordpress/index.php/2025/10/25/rethinking-error-correction-more-effective-pathways-for-grammatical-development/
Note that I've used language like "typically," "traditional," & "most methods," to describe error correction practices that don't work. Now this is reflected in LLMs the typical corrective feedback that they tend to generate, i.e. LLMs, machine learning, Bayesian inference, etc., are engines of "regression towards the mean," i.e. their models "average out" to the most common consensus of responses and texts about a given topic or question, which in the case of explicit form-focused corrective feedback, isn't a particularly helpful one. Yes, an LLM will confidently churn out lots of feedback, guidance, & advice but it will be based on erroneous information about what actually helps language learners.
What's more, preliminary evidence of the effects of using LLMs while studying/working appears to show strong detrimental effects on cognitive development, e.g. the infamous "cognitive debt" pre-print study that got the press' attention. & you've probably guessed it, yeah, I wrote a blog post about that too: https://matbury.com/wordpress/index.php/2025/11/23/report-the-cognitive-pedagogical-implications-of-generative-ai-in-education/