I think there are plenty of studies that can show how many items people can keep in mind, but all that is short-term memory and depends on how well people can chunk information.
For your question, however, I don't believe there is a definite answer. As with all things in UX, it depends on your user: are all 2000-4000 icons exposed to all your users, or are certain icons only applicable to some of your users? (I really do hope it is the latter).
2000-4000 icons of course is excessive, unless you are dealing with subsets created for specific use-cases where there's a different user group. I would split this number into how many different icons one user group has to deal with. Then it has more meaning.
A screen may seem very daunting, when full of indicators and icons, but it all depends on the context and the expertise of the user. When you need to create views for complex situations, where your users needs to have good overview of all things happening, it is often not possible to always show text. But let's make one thing clear: 1 user can not possibly remember 2-4k icons for 1 UI. It would be like having to learn another language.
If your case is indeed with subsets of users (and thus subset of icons), then start by listing all different states and indicators that one such users needs to keep overview with. Why they need it (are things combinable?) and then decide if you need to keep such a status-indicator, or if you can change it because you may merge it etc. Details can always be provided in detailed views.