I have been reproducing it for an hour now on both high and low-pop servers, so I can only suppose that it must be some client-side issue.
EDIT: I reproduced it twice more, only this time I timed how long after I spawned in I got kicked, it seems to be consistently 150 seconds.
EDIT 2: Further testing has revealed that I am in fact able to interact with objects, but while I'm in the server I receive no feedback. I only know if I've picked something up or moved an item in my inventory after I'm kicked from the server and can enter a new one