The discovery of the stars in the observable universe is a daunting task. A 2010 study (van Dokkum & Conroy, Nature 468:940–942, doi:10.1038/nature09578, closed source) estimated that around 300,000,000,000,000,000,000,000 stars may exist.
The largest estimate of the number of biological species is 1 trillion (including microorganisms; Locey & Lennon 2016, Open Access). That is, there are perhaps 300,000,000,000 times more stars than biological species on Earth (Note: the comparison is only partly valid since stars are individuals, species classes with many more individuals; however, it compares the numbers of objects of interest of the given sciences).
The naked eye can see between 50 and 45,000 stars, a good private telescope may detect 380 million stars, and modern scientific instruments can, in principle, record the entire observable universe. The 2018 Gaia data set recorded 1.7 billon stars (and, importantly, including parallax/distance information for 1.3 billion stars).
I ask myself, what we might learn by comparing the inventory and collection efforts of astronomy and biology.
Firstly: Although vast collections of historical astrophotographs exist which have greatly contributed to past discoveries, only some of our current advanced state of astronomical knowledge is not based on historical photographs, e.g. the study of supernovae. For the star catalogs itself, astronomy has focussed on developing and using new, sensitive and efficient technologies, like the Hubble space telescope. The results were scientifically very valuable digital astronomical collections. Historical collections have doubtless value, but it is a mistake to identify the term “collection” with “history” or with the kind of objects customarily collected in the past centuries.
Secondly: Astronomy has not cataloged all observable stars. Instead, the researchers focus their limited resources on interesting questions. I believe we should do the same in biodiversity. In no way should we be ashamed that we do not have a final species catalog yet. We do need taxonomic reference systems, but they need to be problem-centric and allow us to focus our resources on preserving biodiversity rather than cataloging collections. I suspect that our desire to record and catalog all biological species on Earth comes from a past time, where the size of the problem was not yet analyzed, and where we believed in near infinite resources for science. I believe we urgently need to reflect this paradigm. We need to focus on the true necessities of an unsustainable world heading into a potentially catastrophic future for humanity.
We cannot gain conclusive evidence from comparing astronomy with biology. But it might be worth taking a look, to test a different perspective.
PS A friend pointed me to the article http://www.astronews.com/news/artikel/2018/04/1804-018.shtml showing that astronomy does builds summary collections with modern methods. Some of this is clearly “just-in-case” work.