Notice how there are 7 startups at the $2B mark, only 1 at the $1.9B mark, and none at the $2.1B mark. To me this strongly implies that entrepreneurs are indeed trying to hit these big round numbers.
This could be an artifact of how these valuations are communicated, rather than the actual valuations. It's common for companies to not disclose their valuation when announcing funding, but for journalists to make assumptions based on rumors and educated guesses - those assumptions make their way in the headlines surprisingly often. What starts as "approximately $2bn, according to our sources", pretty soon becomes "$2,000,000.00" in an analyst's spreadsheet.
There are 10 employees with 140k salaries at my company and 5 with 150k but none with 139k or 147.26k. People like round numbers, especially when you consider significant figures and how speculative the valuations are. Airbnb could realistically be with anywhere from 500 million to 30 billion or more. The current valuation is a largely bullshit arbitrary number that VC and founder agreed to for God knows why in their latest negotiations. In these negotions you don't counter for 5 or 10% more. That isn't within the significant range.
All things equal, 2.1 gives slightly less dilution to current shareholders but the same positive "optics" as 2. Likewise, 1.9 gives slightly more equity to the VCs but a lot less prestige to the company their investing in (so arguably they get less value).
The same psychology comes into play when pricing anything else. We price things at $1.99 rather than $2.00 because there's an irrational feeling that a price starting with a 1 is much less than a price starting with a 2.
I think the OP is just making the point that a lot of these $1B companies are priced as such because it gives some extra legitimacy, thereby increasing their chance of success and increasing the value of the VC's share. The question is whether this is speculation or whether investing at that price actually makes the company worth that price.
