We have implemented this suggestion. Now the filter configuration (column names + column filter settings, such as min/max) gets saved when the filter is closed, and applied next time the filter is open. This only works within one session, and is not persisted with the project.
This improvement does not address this issue: How to display selected rows after closing the filtering panel?, as it requires a deeper redesign of both the internal mechanics as well as the UX. It is on our radar though.