Flat, monochrome icons emerged due to the hardware requirements of mobile devices with wildly differing DPI.
There can be multiple reasons. But iOS went 6 years with skeumorphic icons (post-iPad, post-Retina) so mixed-dpi screens probably weren’t the only factor.
At that time iOS had the luxury that its higher-DPI variant was exactly twice the original resolution, so up- or downscaling of non-vector graphics worked well. (Similar for macOS.) Moreover, the original iPhone resolution was already relatively hi-DPI, meaning that accuracy on the individual pixel level wasn’t as important as on the typical 96-DPI desktop screen.