Serverless is an easy way for startups to overcome one of the harder technical challenges: scalability. This is purely anecdotal, but the majority of startups I've seen - including my own work - do not have the time or expertise to build out robust auto-scaling systems. They also don't have the money to dump onto a bunch of servers they can fall back to when needed.
But auto-scaling is arguably more important for startups than for well-established companies. Thanks to the unpredictablity of some random high-visibility influencer or journalist sharing your product without notifying you, it's easy for smaller startups to suddenly get hit with traffic that they can't handle with whatever infrastructure they have in place. Sometimes you only get one shot, and if a hundred thousand people hit an empty 503 page on their first visit, they may not come back for another try. Serverless design greatly mitigates that problem.