As the maintainer of an internet facing application, it's part of your ongoing responsibility to, for security reasons, continuously integrate upon your dependencies.
Nothing's fire and forget, it's not sensible not to stand on the shoulders of all these giants around us, but when we do we have responsibility to integrate their security fixes and not break our apps.
Not sure where you draw your line of what"modern" software is when not even system packages and package managment are safe when we have Heartbleeds and ShellShocks, Kernel Vulns et al.
Unless you just mean the bros pumping out new NPM modules/Rubygems/etc, half-assing SemVer, disregarding compatibility as a goal, and only releasing fixes (security-related even) for the latest major version that came out several months ago, or abandoning them. Yeah, that's some serious BS and I hope things mature.