SANTA MONICA, Calif.—Earlier this year, Snap Inc. chief Evan Spiegel was pressing his team to launch a redesign of the company’s Snapchat app. The executives and designers repeatedly responded with an urgent message: We need more time.

Mr. Spiegel had unexpectedly dropped the redesign plan on them in late 2017. After a visit to China, he decided the messaging app needed an overhaul inspired by trends he saw there. It was a quintessential Spiegel decree, say people familiar with the episode—a gut decision without seeking input...