Nick,
I've inherited a number of sites with this same problem, some of them quite large sites with rampant singe-keyword landing pages that required a lot of cleanup. In my opinion, in the long run it's definitely worth the effort to prune where you can and get same/similar content combined into one higher quality page. I've had pretty good success in combining pages into topical focused LPs.
There's been a lot of talk in the SEO world over the last year about "topics, not keywords", and this discussion is exactly where that idea comes into play. With Google's increasing effort at better understanding keyword intent, they've gotten really good at determining synonymous phrases. As a result, sites with single-keyword LPs are suffering (or will eventually) due to content cannibalization. Let's say you have a LP for "blue widgets" and another for "widgets that are blue", eventually those 2 pages are going to compete with each other and Google will choose to rank neither very well.
If you do go down the road to combining pages, here's a few tips:
- Look in Google Analytics for page metrics like organic entrances, conversions, whatever other KPIs are important for you site
- Check Moz metrics like Page Authority and links
- Grab bits of content from the pages going away - just because the overall page is lower quality than others doesn't mean it doesn't have some good content you can
- 301 redirect the old pages to the new one so search engines, people, and links will still lead to relevant content
- Update internal links and your XML sitemap to reflect the changes
Hope that helps, happy optimizing!