(Two other solutions exist. One is spinning the window, you'll see it on ships. The other is making the window hot.)
Many airliners already use heated window panes for de-icing. Heated windows don't work all that great in a downpour, and wiping is a simple and faster acting alternative.
Blasted air is used minimally for windscreens, but it's a common plane de-icing method for the rest of the vehicle.
The complexity and weight of using spinning windows on planes makes that idea a non-starter.
hydrophobic coatings are also in use, but are generally avoided for the duty of primary windscreens due to most hydrophobic coatings lacking durability to physical stress and contact.
The wipers are costly in terms of excrescence drag, and if there was a better way they'd do it.
An example, as used for machine tooling but the exact same mechanism used on ships: https://www.youtube.com/watch?v=YPVBnBK09OM
There are two more solutions I can think of: hydrophobic coatings, and blasted air. I believe these both perform quiet well in less intense rain. Unfortunately both of these suffer from performance degredation from dirt/bug/bird poo etc, so not a perfect replacement to a traditional wiper.
Or using a monitor for the 'windshield' and cooking up some way to keep the camera lens clean.
Put it behind a piece of glass?