I don't want to restrict the subreddit, for one. I have around 295k followers on Tumblr; I can't hand-approve all of them. Plus, restricting the sub would keep new people from finding it.
Plus what the other commenter said about formatting and poor workflow. The mods can just barely handle the current workload of reviewing ~30-40 posts per day, choosing 20 to post, and adding tags as needed. If we had to open an email, then open a link (and hope the link was functional and not malicious), then review the submission, then copy the submission, then open the "submit a post" dialogue, then paste, then format, then post... yeah, that's way too much.
There's an IFTTT workflow for sending Tumblr posts to Reddit, but unfortunately the API it uses doesn't preserve any formatting, so you end up with a giant text blob. I don't think it could handle image posts. If that worked, I'd happily start sending things to a subreddit.
Restricted subreddit means that only approved users can post, but anyone can view. Private means that only approved users can view.
Another option is to set all posts by non-approved users to be automatically flagged (hidden to non-moderators), and moderators can un-flag the posts. Which, I think, is the workflow you're looking for? All you have to do is set the spam filter to "All" in the subreddit settings.
You still run into the problem that a lot of people might not want to use reddit, and you'll just end up fragmenting the people following your blog and lose a lot of readers.
The flag workflow is the closest I've seen on any platform to Tumblr's submissions, for sure.
The concern about people not wanting to use reddit is definitely a big part of this. Reddit has a very different culture than Tumblr, and I agree that it's likely I'd fragment my readers and lose most of them. As much as I love my blog, I don't think the effort of trying to make the switch to reddit is worth the harm and disruption it would cause.
Plus what the other commenter said about formatting and poor workflow. The mods can just barely handle the current workload of reviewing ~30-40 posts per day, choosing 20 to post, and adding tags as needed. If we had to open an email, then open a link (and hope the link was functional and not malicious), then review the submission, then copy the submission, then open the "submit a post" dialogue, then paste, then format, then post... yeah, that's way too much.
There's an IFTTT workflow for sending Tumblr posts to Reddit, but unfortunately the API it uses doesn't preserve any formatting, so you end up with a giant text blob. I don't think it could handle image posts. If that worked, I'd happily start sending things to a subreddit.