Make has dated syntax and conventions. When developers use emojis in command line, support for the spaces and other quirks look worse than a decade ago. Despite all of its expressive power and speed, Make is not going to attract many frontend developers.
If the concepts behind Make are repackaged in a more hipster way, the resulting tool may get far more appeal. Shake https://shakebuild.com is a build system library that can naturally express even the dependencies that require Makefiles go meta and generate new Makefiles. It can be a robust backend for any build system DSL.
I suggested making new build system that has the power of Make or Shake and is still oriented toward frontend development.
You are right that Shake and most general purpose build tools are out-of-touch with frontend. Even for people who are comfortable with these tools, they are not necessarily better than Webpack for the typical frontend tasks. Shake place in this hypothetical tool will be at its backend - like LLVM is the backend of many compilers.
If the concepts behind Make are repackaged in a more hipster way, the resulting tool may get far more appeal. Shake https://shakebuild.com is a build system library that can naturally express even the dependencies that require Makefiles go meta and generate new Makefiles. It can be a robust backend for any build system DSL.