Instead of displaying all JIRA projects in a box on the left-hand side, I suggest that only the projects where you are the project lead should be displayed in a box (as it is currently) and all remaining projects displayed as a list (project name only) below that.
This change would help in our situation where we are a team of 8 developers supporting about twenty applications, which means 20 JIRA projects, which takes up a fair amount of space. Currently you need to scroll down the home page to find the relevant project.
One way to implement this so that it does not impact on organisations with few JIRA projects is to display the projects where you are project lead first and other projects following. If there are more than a certain number (say 5) of total projects, then the remaining projects are displayed as a list of project names. The number of project boxes to display could be a user profile setting as it really depends on their screen resolution. This would cover all bases.