Update: the system described below is live for all past and future elections
Big thanks to Ol' Slim and his merry band of stats-obsessed voters over on Mathematics Stack Exchange for coming up with this brilliantly simple idea. Per venerable tradition, details on how each line-item contributes to the total score are displayed via title-tips - hover your cursor over the line to see which badges are involved.
Original answer: rationale for not implementing this as-requested
The big issue I have with this is that we're making a value judgement on something that's... Pretty iffy all around. We want folks to flag truly problematic comments, just as we want them to flag truly problematic posts. As you note, it's easy enough to "farm" flag counts by flagging worthless (but not overtly problematic) comments, but it's also easy enough (on larger sites at least) to do the same thing with VLQ or Not Answer flags. Heck, there are folks who've built up respectable flag counts via tools that quickly identify spam - do we want to strip this down to counting just Other flags?
I think we're throwing the baby out with the bathwater here. The real problem is that a raw count doesn't say much... In fact, that was my rationale for not including a count for reviews - but this suffers from the same problem, in that most folks won't do what I wanted there either (look at the actual reviews, form an opinion on the suitability of the candidate from them).
An intentionally hobbled score
Some Math users came up with an interesting idea during their last election:
... it resulted in the "Citizenship Score" query, which ranks users on the scale from 1 to 40 as follows:
1 point for each 1K reputation, up to the maximum of 20 points. Users below 1K rep are not included.
1 point for each of the badges Civic Duty, Cleanup, Constituent, Convention, Copy Editor, Deputy, Electorate, Enthusiast, Explainer, Investor, Marshal, Organizer, Quorum, Refiner, Reviewer, Sportsmanship, Steward, Strunk & White, Tag Editor, Yearling. (Each badge is counted only once.)
The purpose of counting these badges is to approximately quantify the contributions that do not result in reputation (edits, votes, meta posts, tagging, reviewing) as well as the level of experience with the site.
I like this idea a lot, because it makes it hard for someone to dominate the list with one statistic (rep, flags) if they haven't done much of anything else. Also, it has the potential to scale a lot better than the current metrics (and restrictions such as those on Stack Overflow). My concerns regarding such a score applied to the general population don't apply to elections, since we're not trying to rank, say, askers according to their flagging prowess - we're explicitly looking for well-rounded - exemplary, even - citizens.
Flag counts aren't public data, so that didn't figure into Math's score - but there's no reason we couldn't include them if we wanted to. We could even cap the influence of each type of flag on the overall score, offering a small benefit to folks who don't fixate on one type of problem. We could lump close votes and close flags together in this, and offer a breakdown for those interested in seeing what a given candidate's "baseball card stats" look like.
Most crucially, this score could replace reputation in the list of candidates, potentially offsetting the natural tendency of some voters to vote according to reputation and nothing else. Imagine if the nominations were signed like this:
This idea still needs some fleshing out, but I strongly believe we'll want to implement something like it for elections in the near future. Particularly with recent changes to flagging associated with Review, the utility of a raw Flags Raised stat has dropped considerably - time to re-think the whole plan.