With respect, I think you need to re-skim that paper.

> Your study seems to be looking at remnants of viruses “left behind” in our collective genome by analyzing datasets.

You appear to be confusing the 'genome' and 'metagenome'. The genome does have plenty of viral remnants[0] that by and large are incomplete fragments.

The 'metagenome' in this case is taken from the Human Microbiome Project[1], which took samples of the microbiome from various regions of the bodies of various humans[2], and then sequenced basically everything in there that they could.

> might not be complete (they remark in the abstract that some have nearly complete genomes).

The only thing about completeness in the abstract I'm looking at is "with historically high per-genome completeness".

Later in the paper they write "A total of 14,034 contigs (31.2%) were estimated to be high-quality (90 to 100% complete)" which I'd call more than 'some'!

> but at the end of the day there’s only so much you can do when you don’t have a live virus to “tweak the dials” so to speak

Many viruses are not currently able to be cultivated. This doesn't mean that they aren't important, or that they can't be studied.

For a different example, consider the anelloviruses. From [3]:
"""
Anelloviruses are small, single stranded circular DNA viruses. They are extremely diverse and have not been associated with any disease so far. Strikingly, these small entities infect most probably the complete human population, and there are no convincing examples demonstrating viral clearance from infected individuals. The main transmission could be via fecal-oral or airway route, as infections occur at an early age. However, due to the lack of an appropriate culture system, the virus–host interactions remain enigmatic. Anelloviruses are obviously mysterious viruses, and their impact on human life is not yet known, but, with no evidence of a disease association, a potential beneficial effect on human health should also be investigated.
"""

The way I read this, you are almost certainly infected with anelloviruses, I am almost certainly infected with anelloviruses, we don't know how they're transmitted, we don't know what cells they target, and in fact we don't know very much about what it's doing in there at all.

> a finite supply

Well sure, and there's only so many hundreds of millions of years before the sun devours the earth.

Hoel writes:
"""
In virology, there are only so many dials—only so many natural viruses. And each is a source of competition, as famous labs make claims to various viruses to study and monopolize them by beating others to publication.
The big excitement is in finding a new virus, mapping the genome, figuring out its function and transmissibility, comparing to other viruses, etc."""

How many virology labs are out there? The American Society of Virology has about 2500 members[4] in the US, Canada, and Mexico. Multiply by 10 to bring in the rest of the world (surely an overestimate, if anything) gives you 25000, which is still less than the number of brand-new viruses found in this one study!

And that's just from a handful of samples focusing on one organism (albeit one of particular interest). Wiki lists 96 families of virus[5], some of which have dozens of subpages. Viruses are everywhere you look, and infect every kind of life on earth including each other[6]

I'm also not convinced that labs can "monopolize them by beating others to publication". Many viruses are worked by many labs. As just a quick example, I searched biorxiv for 'herpes' (it's a virus!) and of the first few papers that looked like virology I found authors affiliated with Cambridge (Departments of Pathology, Veterinary Medicine, and Medicine, as well as the Institute for Medical Research) [7], the European Molecular Biology Lab [7], University of Berlin [7], University of Columbo [7], LSU [8], Albert Einstein College of Medicine [9] (Departments of Microbiology and Immunology, Pediatrics, and Medicine), Institute for Virology (Zurich) [10], University of Bern[10].

This doesn't seem like monopolization to me.

> quality of genomes will likely further reduce this number

14034 new genomes is still an awful lot, and so is the text in this post, so I'll stop here.

[0] https://en.wikipedia.org/wiki/Endogenous_retrovirus
[1] https://hmpdacc.org/hmp/publications.php
[2] https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5831082/
[3] https://academic.oup.com/femsre/article/44/3/305/5809966
[4] https://news.cornell.edu/stories/2021/04/cornell-virologist-...
[5] https://en.wikipedia.org/wiki/Category:Viruses_by_family
[6] https://en.wikipedia.org/wiki/Sputnik_virophage with a bit of poetic license.
[7] https://www.biorxiv.org/content/10.1101/2021.04.13.439638v2....
[8] https://www.biorxiv.org/content/10.1101/2021.05.05.442792v1....
[9] https://www.biorxiv.org/content/10.1101/2021.05.05.442792v1....
[10] https://www.biorxiv.org/content/10.1101/2020.12.23.424160v2....