Eric Schiller, a software engineer in Alexandria, Va., thought the job offer sounded pretty straightforward. A boutique insurance company wanted him to bundle its various financial departments into a single, modern, shareable data platform.

At the time, the company’s actuaries were running their statistical analyses and risk calculations on a specialized Excel spreadsheet that nobody else could access, let alone comprehend. Mr. Schiller figured this would be an easy fix. “They’re mathematicians,” he told himself. “They think...