Even in a quiescent state, DNA is bound to a lot of proteins. It is not a lone double-helix of DNA with an occasional protein attaching here or there. Rather, it is tightly wrapped around histones, which themselves have other proteins attaching and detaching constantly. Repair enzymes are always whizzing about and fixing the random damage that occurs in DNA naturally, and transcription factors may be sitting on the DNA for a while and then diffusing away again without doing anything. There are probably more proteins around that I've forgotten.
As you can see, the nucleus, DNA and in general the cell interior are extremely crowded spaces, and for transcription to happen it takes more than just removing some TFs attached to intronic sequences. Histones need to be modified to repel each other and make space. Ultimately, all proteins will need to detach for a short time when RNA polymerase comes through. If they don't, polymerase will stall until they move away, or it may simply fall off, producing an incomplete RNA fragment which will be degraded quickly. Another polymerase will come along soon enough and produce a new transcript if the promotor is still in a permissive state.