"The admins should allow themselves some room for individual judgements on a case-by-case basis. The admins need to have some leeway for discretionary actions."

The Admins/Mods have this leeway already: At any time, they can forgo the usual process and outright ban someone if they determine the actions warrant it.

The warnings, IMHO, are for Members who have not crossed the "instant ban" line and deserve a chance at proving themselves. Therefore, it seems reasonable to me that, after they have proven they can "play nice", the lesson is learned and the warning should be removed.