Asking for critique is off topic. Asking for how to improve your writing is on topic.
What is the actual difference? In both cases the person asking provides an example of their own writing and asks for help improving it.
There is a site proposal to address the lack created by the prohibition of asking for critique, but I'm convinced it won't take off. And I see that some members are very skilled at cloaking their requests for critique by embedding them in a more general question and providing an "illustrative example" from their own writing in such a manner that if you answer the general question you will edit the sample to illustrate your answer, effectively providing the editing that this site forbids to ask for.
Why don't we just make this on topic?
For one, I really feel that the critique of an individual text still gives me a great learning experience when I read it, even though it appears to be limited to that specific text at first glance.
Secondly, I feel that Stack Overflow, the godlike image that all other sites are created after, does just that: it is perfectly on topic there to post part or all of your code, say it doesn't work, and ask for help. It is off topic on SO to ask people to code for you, but it is on topic to ask for pointers on what is wrong with your code. All that is necessary is that you show that you tried to solve your problem yourself.
Folling that example, I think it should be on topic here to post all or part of your writing, say that you feel it doesn't work, and ask for help in improving it. People can then post (partially) corrected versions of (part of) the text, explaining what they did and why, helping the person asking to understand and then implement this understanding in further improvements.
The only limitation I would set up is that people asking questions don't just post text and ask to "correct that". Requests for corrections should remain off topic. But this limitation will implement itself, as it does on SO, where people simply do not give answers or vote to close when people don't show any initial work of their own and try to abuse the generosity of the community.
I would therefore propose to experimentally make requests for critique on topic for a limited time (say, three months), effectively merging the site proposal with Writers, and at the end of the period evaluate our experience with that experiment.
If requests for critique begin to overwhelm all other content, or if we dislike it for some other reason, we can easily make critique off topic again.
Here is an old discussion: How are critique questions working out for us?
As for the objection that looking at the bad writing of others doesn't help anyone else, I want to point out that:
helping in improving that writing is some of the best writing exercise you can do, and
all sites, but mostly Stack Overflow, are full of questions that are so limited that they will be useful to almost no-one or that have become obsolete because they address (versions of) software that is no longer in use. Everyone on SO knows that every question on that site will become obsolete eventually, yet they are not made off topic for their future uselessness. There is no reason we need to make something off topic here because in the future it will no longer be of use, either, it is enough that it is of use to everyone taking the time to answer that question.