No, I don't think letting nature take its course is the answer, but there might be another approach.
You could, as Hutch42 suggests, inventory existing URLs and then gather some additional information, meaning inbound (landing page) traffic and links.
- If a page has inbound traffic it usually means the page is ranking well, bookmarked, linked to or shared. No inbound traffic means people come to the page after having already landed elsewhere on the site.
- If a page has incoming links, that's helping build your domain authority.
Group pages according to the ones that are getting a significant amount in inbound traffic or have inbound links. Redirect those. Don't bother with the others.
Google analytics will tell you which pages have landing page traffic. Use a couple of different link tools to assess which ones have valuable inbound links including Google Webmaster Tools. (Every tool is going to give you a different answer. You want as good an inventory as you can muster.)
How much is "enough" inbound traffic and/or links? That'll be a judgment call on your part. So really you'll need to weigh the amount of effort to do this analysis versus the amount of effort to build the redirects and go from there.
That's my two cents.