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 Village Pump proposal (http://en.wikipedia.org/wiki/Wikipedia:Village_pump_%28proposals%29#Being_able_to_edit_your_edit_summaries) with currently only positive responses.
There is a also somewhat related closed bug (https://bugzilla.wikimedia.org/show_bug.cgi?id=10105) which did not discuss reasonable restrictions or implementation details. The current proposal addresses previous objections such as increased user interface, system, or code complexity.
This card tracks a proposal from the 2015 Community Wishlist Survey: https://meta.wikimedia.org/wiki/2015_Community_Wishlist_Survey
This proposal received 43 support votes, and was ranked #19 out of 107 proposals. https://meta.wikimedia.org/wiki/2015_Community_Wishlist_Survey/Miscellaneous#Technical_user_right_to_edit_summaries