The button will not appear if there is no primary risk selected and supplementary risks are also configured to be "only blank".
If there is a primary risk type in the project settings, then that's the issue type selected by default on the Create Issue page.
If there's no primary risk type in the project settings, and one or more supplementary risk types are defined in the 'Only' category, then the first of those supplementary risk types is selected by default on the Create Issue page.
If there's no primary risk type in the project settings, and the supplementary risk types are defined as 'All except', then the first issue type available in the project and not explicitly excluded is selected by default on the Create Issue page.
If we're working with a multi-project risk register, then we:
a) look for the first project (sorted alphabetically by project key) that has a primary risk type defined; OR
b) if none of the projects define a primary risk type, then we look for the first project that has a supplementary risk type defined, whether explicitly via 'Only' or via 'All except'.