They never did.
If you use the definition of a startup as "still searching for a business model" and not "any company of any age and size as long as it's involved in technology", then there's no reason for them to apply for a patent.
By the above definition, startups haven't yet figured out what is their exact product, what is their business model etc. There's nothing there to protect with patents yet.
And what also follows, they're not successful yet so no-one will sue them for patent infringement. Lawsuits are about money. If there's no money to extract, there's no point in suing.