Large projects have dedicated QA teams that would benefit from knowing how well they are doing in attending to the project's bug reports, and in closing them. Launchpad would be the ideal place to do this, but currently it doesn't.
Both current and potential contributors can also be motivated to work on a project or package by seeing how quickly (or otherwise) bugs are dealt with in that project/package. (For example, Colin Watson in <https://lists.ubuntu.com/archives/ubuntu-devel/2008-October/026729.html>: "I've found that seeing the bug graphs at http://people.ubuntu.com/~bryce/Plots/ drop can be a great incentive when I'm working on a package's bugs.")
One way of doing it would be two cumulative frequency graphs on the project's Bugs page. The first would graph percentage of bug reports against time taken for report to first change state (e.g. New->Confirmed). The second would graph percentage of bug reports against how long before the report was closed (i.e. Invalid, Won't Fix, or Fix Released).
A simpler way would be a single stacked bar chart showing, for the past few months, the number of bug reports that remained in each unresolved status on each day; and below the X axis, the number of reports that were resolved in each way (fixed, declined, or marked as a duplicate) on that day. https://launchpadlibrarian.net/98323734/graphing.png
Probably it would save time to fix bug 37926 at the same time as doing this.
A future enhancement would be to show change over time on the same graphs. For example, the current distribution could be shown with a dark solid line, while the distribution six months ago used a lighter dashed line, and the distribution a year ago used a lighter dotted line. This would make it easy to see if a project had improved its QA processes.