Okay, now I understand what you mean. I think this is possible by combining the URL parameter with the user interface input field.
Instead of using the "Fixed location" radio button, you can do the following:
1. In the Query Filter dialog shown in your screenshot
Select the third option: Distance center is set using URL parameter, and leave the value as toolset_maps_distance_center.
This is the parameter name used to pass a center location to a distance filter, so it must be exactly the same.
2. In the Search and Pagination section
Click New filter and add the Distance filter.
This renders the front-end address field and radius control that visitors can use. It submits the address using the toolset_maps_distance_center parameter, which the Query Filter configured above will use.
If you do not see the Search and Pagination or Filter Editor sections, open Screen Options in the top-right corner of the View editing screen and enable them.
3. View settings
Set the View to Display the results as a custom search.
In Custom Search Settings, enable AJAX results update when visitors change any filter values. This will refresh the results and the map as soon as a visitor enters a new address, without reloading the page.
4. If you combine this with other filters
Set Should distance center input be required to No.
I believe this should provide the functionality you described.
Please review the following documentation about maps first:
https://toolset.com/documentation/legacy-features/maps-plugin/filtering-and-ordering-map-markers-by-distance/
Then review this documentation about Views:
https://toolset.com/documentation/legacy-features/maps-plugin/how-to-display-custom-search-results-on-a-map/
Thanks.