Just wondering if there is a way to set up dataset collections (member pages, not dynamic) and assign files to owners (members)
Yes
You can create your own Member Account Page called ie My Files, have a Data Collection with a File Field and then an Upload button on the member page Files connected to that dataset and field. Then you can have a repeater or table on the page which lists their files. Just set Filter on The Dataset to be _owner = Logged in user