Currently, every frontpage except for the Stack Overflow frontpage shows the most recently modified questions sorted by the modification date. This means that old questions are bumped to the frontpage when edited, sometimes a lot of them at once when a tag is cleaned up.
The main purpose of that is to ensure peer-review of all edits, to prevent someone from performing misguided or malicious edits without anyone noticing it. This peer-review is important, but anonymous users don't participate significantly in it. Theoretically they could via suggested edits, but as far as I've heard the number of valid suggested edits from anonymous users is negligible compared to all other activity on SE sites.
So why are anonymous users seeing a frontpage that is selected and optimized with a goal in mind that isn't really relevant to them? Why don't we show them a frontpage that is optimized for them?
The frontpage for anonymous users should show in my opinion the most recent, good questions from that site. That is the goal the frontpage should be optimized for, e.g. by the following criteria:
- Don't show closed questions (anonymous users can't flag or vote to close)
- Don't bump old questions that are only retagged, or maybe even don't bump old questions at all (except for the community user bump)
Those are only some ideas, there might be other aspects one could change.