This answered it for me (directly from the wheel PEP):
Python needs a package format that is easier to install than sdist.
Python’s sdist packages are defined by and require the distutils and
setuptools build systems, running arbitrary code to build-and-install,
and re-compile, code just so it can be installed into a new
virtualenv. This system of conflating build-install is slow, hard to
maintain, and hinders innovation in both build systems and installers.Wheel attempts to remedy these problems by providing a simpler
interface between the build system and the installer. The wheel binary
package format frees installers from having to know about the build
system, saves time by amortizing compile time over many installations,
and removes the need to install a build system in the target
environment.
https://www.python.org/dev/peps/pep-0427/#rationale
Note the tarballs we’re speaking of are what are referred to as “sdists” above.