I’m not clear what it is you are asking for here. As @m_whitson said above, the genus level observations are recorded by the projects. They are also displayed in the Observations tab on the project pages, but you will have to scroll down a ways to find one. If you click on “search” on the Observations tab for the NPS – Lake Mead National Recreation Area project, and search for genus Tamarix, you will (at this time) see 224 observations, of which 85 are ID’d only to genus.
The only place I can see where they are not displayed is in the “Species” tab which lists species in order by number of observations. If this is your concern, then the project admin’s can do nothing about it – that is the way the Species tab is implemented in iNaturalist. There is an existing Feature Request to modify this behavior: https://forum.inaturalist.org/t/sort-the-species-tab-by-higher-level-taxa/3043/10