The power to view these posts is given along with the power to delete and undelete. You can't undelete if you can't see deleted posts. This power is granted at 10k. There isn't significant value in these posts (from a stackoverflow perspective) and they don't belong on stackoverflow, so giving the power to view these posts earlier than the power to delete and undelete makes little sense. It's a community moderator ability.
They are only visible to those that have significant experience with the system for several reasons:
- Sometimes a question is deleted by the question owner (for a variety of reasons) and they don't want just anyone poking around their deleted material. Perhaps it embarrassing, or perhaps they stepped over a legal line with some NDA.
- Many questions are deleted to stop discussion on a given topic, and several are very incendiary. By allowing those with little experience and trust in the system to view them, we are inviting further discussion and unhappiness.
Those that have demonstrated significant experience with the system are privileged to see them not to gain information from them, but for the purposes of moderation. They are expected to evaluate them and undelete them when appropriate. It's another level of moderation, but like all other levels of moderation you can only gain it after the community trusts you to do so by upvoting your other contributions.
There are closed questions which are easily searchable on the site, and also accessible through the data dump. These are visible to everyone, and are as relevant as the site allows. Those questions that are deleted are not meant to be part of the stackoverflow corpus.