Any time you use an inserted row or column in a UX view and populate the values with a custom formula then by definition we assume that the cells are reference values and are read only. This also applies to DBRW formulas which as they are read only also don’t display a picklist or allow data entry.
Rather than using an inserted column with DBRW maybe you can join multiple views in a single table to get the layout that you want. Then picklist and data entry will work.
If you need the DBRW formula to be writeable then this would be a enhancement request as this isn’t currently supported.