You write: However, RNA polymerase 2 is just a protein that transcribes genes. Why do we care about where it is (i.e., where it is bound) at the moment chip-seq is run?
The very point of histone modifications, transcription factor binding, the binding of pausing, elongation, and termination factors, etc is to regulate gene expression, and Pol II is the very machine responsible for protein coding gene expression in eukaryotes. Those studies linking the role of some histone modification, nucleosome position, factor binding, chromatin state, etc. to transcription would be better served including an analysis of the location of Pol II, and depending on aspects of the way the experiment was conducted, such knowledge may actually be better than an expression array or RNA-seq data.
Further, Pol II is not, "just a protein that transcribes genes," but rather it is arguably THE regulatory nexus for development/stimulus-response networks/homeostasis or whatever. Think about it; pol II is at once the terminal receiver of any signalling event regulating protein coding gene expression AND the initial step in the response to said event. It is very literally the inflection point between stimulus and response! This protein is itself highly modified in order to coordinately regulate every step of the transcription cycle (initiation, pausing, elongation, termination, recycling of the polymerase for subsequent transcription) via myriad post-translational modifications that we have only begun to understand. Pol II recruits factors to itself involved with all the aforementioned steps as well as RNA processing and histone modification. It is far more the supervisor of a factory than it is "just a protein that transcribes genes."
In higher eukaryotes Pol II is regulated post initiation, via promoter proximal pausing, and the position of Pol II at promoters relative to gene bodies is revealing in ways that are difficult if not impossible to appreciate using data derived from RNA-seq/microarray or nascent transcript sequencing which fail to accurately juxtapose promoter vs gene body Pol II levels in ways that reflect biology.
Could it be that RNA Polymerase binds to TSS and knowing the TSS can be helpful? Genuine loud thinking because I'm bad at biology.