Hi there,
Nothing really as it relates to an "out-of-the-box" type solution with a setting or anything through Cube views. From a simplicity standpoint, the cleanest way would be to have users save their most commonly used POV as a favorite, and then reference the user's POV parameters as the default in the Cube View.
If you're displaying the Cube View as a component in the dashboard, you can use "BRApi.State.SetUserState" to create essentially a name-value pair for the user and their associated last-used UD1/2/etc. - but this would require the parameters to be updated on refresh of the Cube View. Those parameters would then follow the user going forward until they change it again. This method is definitely takes a lot more up-front work but if you have a huge user-base that won't want to mess with favorites it's worth exploring.
Short answer - no default feature or setting to do this - first option would be using favorites unless you want to throw in all the bells and whistles.
Thanks!