Background
At present, on submission of edits to MediaWiki, the edit summary and minor-edit status is fixed, so cannot be changed.
These are key metadata about the edit that is displayed in a page's edit history, in a User's user-contributions, and in Special:RecentChanges. Edit summaries are invaluable for tasks such as understanding work on Wikipedia, building datasets of edits for study, and contextualizing edits.
For background, also see T287992: [medium] Understand current usage of edit summary statements on Wikipedia.
Edit summaries however may not be accurate. Vandals may provide misleading summaries and many editors leave the summary blank or use a canned edit summary that may or may not accurately reflect the impact of the edit. Users often report submitting an edit and immediately regretting not leaving an edit summary.
Proposal
It should be possible to change edit summaries after they've been submitted. This would allow the original editor to change their edit summary after the fact. It would also allow admins to change any misleading edit summaries, or add edit summaries where they are missing.
Let's talk about changing edit summaries rather than "editing" edit summaries, as then "editing" can exclusively refer to changes made using action=edit, to avoid potential confusion.
It should also be possible to mark or unmark edits as minor.
There may be potential for automation or semi-automation of this with AI. Modern AI is now very good at comparing the differences between two texts and summarising those differences. Note the AI is not proactively generating content here by itself, but reacting to human-generated content, which should avoid major hallucinations and thereby avoid genuine concerns regarding insertion of incorrect hallucinated information into wiki pages. See T326595: [long] Train model for auto-generating edit summaries.
Outline scheme
Here's an outline of how this could be implemented:
First, you'll need some user rights. Registered users can probably be trusted to change their own edit summaries (changeowneditsummaries). Admins can be trusted to change others' edit summaries (changeotherseditsummaries).
Second, you'll need a log -- i.e. EditSummaryChangeLog. This should record the Revision ID, the user ID and username of the user who made the edit, the user ID and username of the user who changed the summary, and both old and new edit summaries. Changes should be numbered to count the total number, and to identify any change. Also, the number of changes made to a particular edit summary should be noted, and could be displayed next to it in page histories/user contributions. Log entries should be suppressible by members of the Suppressors user group, in case anything legally problematic finds its way into the log (suppresseditsummarychangelogentries).
Third, you'll need a special page at Special:ChangeEditSummary that will take a revision's RevisionID, so Special:ChangeEditSummary/1234567890` would allow a change to be made to the edit with revisionID 1234567890 (whatever that is).
Fourth, in logs where edit summaries appear, i.e. user contributions, and page history, new page log (are there others?), we'll need a "change" link after the edit summary. This would enable that summary to be changed. It should be visible only to users with permission to make changes to that summary (i.e. admins and the editor who made the edit).
Deal with any other issues that come up.
Implementing this is likely to be a fairly large (Epic ) project (see comments below). There are also some concerns about cluttering the UI. Using AI to generate summaries for 25+ years of Wikipedia edits would use lot of computing power (i.e. electricity, water -> environmental impact), so enabling this might not be the best idea while computational power load for AI remains high. Any implementation attempt should bear these objections in mind.
Background to requests
Something like this has been proposed for a long time.
This card tracks a proposal from the 2015 Community Wishlist Survey: https://meta.wikimedia.org/wiki/2015_Community_Wishlist_Survey/Miscellaneous#Technical_user_right_to_edit_summaries
This proposal received 43 support votes, and was ranked #19 out of 107 proposals.
Original 2008 description:
I propose to implement a mechanism to correct edit summaries (1) if it is your own edit (2) and if it is the last edit (3) during a short time span (e.g. 1 - 12 hours).
One possible way to do this would be a link on history pages, e.g. "(rollback | undo | fix summary)". A new page would then allow to fix the summary.
Such a function would allow to fix accidents such as empty summaries, switched summaries (when you have many tabs open), and half-completed raw summaries. Currently, minor or fake edits are required to provide a correct summary.
Under the proposed restrictions (own, last, recent), there is probably no potential for abuse (e.g. any following edit would make the previous summary permanent). This would allow to simply overwrite the edit summary field without the need for a summary history or log.
This might have to be restricted to registered users as theoretically an anonymous user with reassigned IP would be able to change summaries not belonging to him.
There is a current [2008] Village Pump proposal (https://en.wikipedia.org/wiki/Wikipedia:Village_pump_(proposals)/Archive_30#Being_able_to_edit_your_edit_summaries) with currently only positive responses.
There is a also somewhat related closed bug T12105: Allow editing of edit summaries after the fact which did not discuss reasonable restrictions or implementation details. The current proposal addresses previous objections such as increased user interface, system, or code complexity.