This technique isn't new. Biologists use it to count the number of fish in a lake. (Catch 100 fish, tag them, wait a week, catch 100 fish again, count the number of tagged fishes in this batch)
You could bucket bugs into categories by severity or type and that might improve the estimate, as well.
I guess it underestimates the number hard to find bugs though since it assumes same likelyhood to be found.
In the "100 fish" example, the formula for approximating the total number of fish is:
total ~= caught / tagged
(where caught=100 in the example)
total ~= (valid / tried) * 2^64
Edit: Oh because 64^10 * 16 = (2^6)^10 * (2^4)
What makes it the "best method"? Would it be better to use a seine, or a trap, or hook-and-line? How would we know if there are subpopulations that have different likelihood of capture by different methods?
To say it's "reasonable to argue that the effect is insignificant" is purely assertion. Why is it unreasonable to argue that a fish could learn from the first experience and be less likely to be captured a second time?
If what you mean is that it's better than a completely blind guess, then I'd agree. But it's not clearly the best method nor is it clearly unbiased.
And, also, the fish gets tagged for its own good.
They'll even call you tinfoil fish.
https://en.wikipedia.org/wiki/Unseen_species_problem http://www.stat.yale.edu/~yw562/reprints/species-si.pdf
Won't this mess up stats though? It's like a lake monster randomly swapping an untagged fish with tagged fish as you catch them.