In our installation we have more than 3000 projects. All of these projects are loaded in browser on each page every time you open any url and 90% of page content is html with project names. We use Favourite Projects Plugin https://www.redmine.org/plugins/favorite_projects which allows to reduce number of projects loaded in project jump box. But in Redmine versions 3.4 and 4.1 there are many great improvements of standard functionality (#23310, #31355) and only one little thing is missing.

I think that projects should be loaded in project jump box dynamically when user typing in search box. By default you can show only N first projects or don't show anything (only bookmarks and recently used projects from #31355).