It's useful if the startup has something it wants to hide in its trademark application (like a product description that it wants to protect) and can justify the added filing fees. But, there are over 1,000 new US trademark filings every day so in most cases, someone would have to be actively searching for it. Also, often the description that accompanies a trademark application is rather broad, so it may be difficult to determine what the application is for without knowing more. Tech companies like Google and Apple are under much more scrutiny.
It's in part a strategy to hide their plans from each other, but it's also to be able to announce their products to the public on their terms and control the timing and pace of the reveal.
You may be able to request trademark application records in those jurisdictions, but I imagine it's more of a process. You would also likely need to know the mark itself or the company filing the mark. In the case of Apple, if they file applications under a shell entity and without knowing the product name, it would be difficult to find the application. Also, given the high number of countries without electronic IP records, there are still plenty of opportunities to hide filings.
That being said, it's likely a loophole that will become increasingly narrow over time as more IP offices go online.
There are also better uses of startup capital than expensive newspaper notices that aren't benefiting the public as the same information is available on state websites. In the aggregate, millions of dollars are being transferred to newspapers each year through this law.
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If a company incorporates as an LLC in another state, New York loses out on the formation filing fees. Also, if the company also chooses to set up its office elsewhere, New York would lose out on additional tax revenue.