I would not leave the whole thing open. That would bring out the worst in your students.
If one week seemed too small, why not try two-week modules?
Yes, going without regular deadlines is not a good idea. I once inherited a "self-study" class (not online, but a precursor), which historically had a 30% completion rate. It stayed that low when I picked it up until I started having deadlines throughout the semester. Completion rates then jumped up to 70%.
Another way for balanced flexibility is to have weekly deadlines plus a few "catch-up" weeks during which you re-open closed modules (or at least the parts that can accomodate go-backs). I have those weeks spaced about four weeks apart (and only re-open the last four weeks of work). Since I always have future content open and available, students can also work ahead during those weeks. We have a lengthy semester here (18 weeks) so I can afford 3-4 catch-up weeks. In the summer term, the catch-up period is just a few days long. The great thing about the catch-up weeks is that you can use them as filler to make the class fit the calendar well (for example, what to do with the partial Thanksgiving week).
I always have all content open for students to work ahead. Very few take advantage of this. But it's absolutely no trouble for me, so why not? I've never understood the reason to withhold content, unless it's the practical matter of not having it prepped yet.