There is another, wholly unrelated, problem that is sometimes associated with collecting all of the data: so-called destructive sampling.
Sometimes, the act of collecting data destroys the object of the data collection. Consider the following question: “How reliable are the matches that I make in my match factory?” In this context reliable means how often they light the first time I strike them. This question is very important to me because I want to market my matches as being of the highest quality. This way I can sell them for a greater price than my competitors’ matches.
But collecting all of the data would require me to strike every match my factory produces in order to test it. This way I would know with certainty how reliable they are. But I would also have no matches left to sell. Collecting all of the data in this case is not an option.