PsychoPy needs to be installed in some way in order for its scripts to run. Python is just a general purpose language: to do the things that PsychoPy does requires a bunch of other libraries to be available to Python (not just the PsychoPy modules themselves, but all of the other external dependencies that PsychoPy requires, to do things like displaying stimuli, playing sounds, connecting to hardware, and so on).
And “just Python” is not a given either: Python exists in Linux, and an old version ships with Mac OS, but it doesn’t come as standard with Windows. And as you won’t know what version the users will have, if they have one at all, they’ll probably need to install a specific Python anyway. And then you still need the PsychoPy related stuff, and installing this into a Python installation manually is not trivial for people who aren’t used to this sort of thing (and even for those who are).
Given that, you might as well install the PsychoPy standalone application (which bundles its own version of Python, as well as all the other dependencies). It’s a one-step process that saves you from all of these hassles.
If you can’t run your experiment online, there just isn’t a practical alternative to installing PsychoPy locally, whether stand-alone or otherwise.