So this morning I was looking for a solution to "force" the user to enter a query on one of the columns - either through the "search bar column list" (the magnifier on the left side of the search field) or through the Actions > Filter menu. The first attempt was to use a Dynamic Action that fires on change of the search field, but that doesn't work when the user switches existing filters on or off. So I inspected the debug output of the page and discovered an item named "APXWS_EXPR_1". This item is set when the report is refreshed and contains the value of the first column filter you apply. Subsequently you can have APXWS_EXPR_2 etc. So I added an additional restriction to the query:
:APXWS_EXPR_1 IS NOT NULL
Thus by just adding one line to the query the user is forced to use at least one column filter - both the "contains" as any other more specific filter works. And I can even delete the previous solution that prevented running the query (actually the query is run, but returns "no data found" in no time) when the user navigates to the page.
As a side note, if you use the general filter on all columns, that value is available on the server as "APXWS_SEARCH_STRING_1" (and _2 etc.)