While I agree that data would be amazing...But, to answer your question "why is this so hard?" The reason it's so hard is that there is almost zero chance of determining who a person contracted it from, or who they passed it on to.
So, you can test Person A, and find out that he is infected with COVID-19. But, to determine how long he is contagious for (and develop useful data) you would need to know exactly when he contracted it, and then when he is no longer contagious. Those are two things that we can't define precisely.
As for your question about viral load, there was a study in the UK. As far as I know, it's the only totally random study of size done (as opposed to compiling data on individuals who presented themselves for testing). They randomly tested 100,000 or so people in the country(ies). What they found is that:
--Vaccinated people test positive half (49%) as often as unvaccinated people (when they reported a recent contact with a COVID-19 positive person)
--Vaccinated people tested postive 1/3 as often as unvaccinated people overall.
--Vaccinated people have a lower viral load than unvaccinated people.
https://www.news-medical.net/news/2...times-lower-for-double-vaccinated-people.aspx