The purpose of bumping a question that gets edited is so that other community members can have a look at it and make sure the edit is reasonable. This is an important community cross-check; even high-rep users sometimes make mistakes and end up making edits that outright need to be rolled back.
There might be a better way to implement this -- perhaps a separate view of the most recently edited posts, instead of bumping them all to the front page? -- but in the implementation that we have at present, I don't see such a "minor edit" option adding much value. In fact, I can easily see it being abused to mask edits that really should see some form of community review. While many -- most, actually -- edits are useful, some (often, these are caught in review and rejected) are outright detrimental or destructive.
There are two ways to approach this that both, IMO, are better than a "minor edit" option, at least in the short term:
- Space edits apart. Don't edit dozens of posts at a time; instead, edit a few, then wait until the next day and edit another few. This prevents flooding of the front page and, assuming the number of posts to be edited is reasonable, still ensures that the edits get done in a reasonable amount of time. Pick the number of posts and the time to wait between edit sprees based on the activity level of the site; Stack Overflow can obviously sustain a higher rate of edits than Worldbuilding without flooding the front page with only edited posts.
- Have an editing day or weekend, to fix issues agreed on by the community needs fixing. This needs a bit of coordination (which can happen through Meta and chat) but can easily make it all go quicker in the end. At least Super User has done this with tag edits where old tags needed to be replaced with new ones; proposals are made on Meta, community agreement is sought, then a time period is picked when the changes are implemented and real-time coordination is done in chat. This largely floods the front page with the edits, but it's for a limited period of time and everyone can clearly tell what's going on. The relevant Meta post can easily be featured for the time period, making it readily visible to those visiting the main site.