Thanks for your helpful answer, Christoph. No, authorizations weren't the problem. I have SAP_ALL. But I've found an interesting "bug". Well, I think, it is a bug.
The transaction types for display in the popup are determined in class CL_AI_CRM_UI_API, method GET_INCIDENT_TRANSACTIONS, with the help of function module DSWP_NOTIF_READ_PROCESS_TYPE. When only one entry is determined, no popup appears, and the corresponding transaction type is created directly.
For Incidents, the entries from DNOC_USERCFG are taken into account, and only these entries are displayed, or when only one entry exists, this transaction type is directly created. This is correct.
But:
For Incident Templates, the entries from DNOC_USERCFG are also drawn, but not as expected.
One entry "PROCESS_TYPE_TEMPL" exists, but it is ignored:
During debugging, you can see, that in function module DSWP_NOTIF_READ_PROCESS_TYPE the entries with fieldname "SERVICE_REQUEST_TEMPL" are drawn and excluded from the list of template transaction types. Afterwards all other determined remaining transaction types are displayed in the popup. I have tested this, and added the following transaction types with field "SERVICE_REQUEST_TEMPL" to DNO_CUST04: ZMRT, ITIT, SMIT, SMRT. Now ZMIT is directly created, when the button "New" is clicked in Incident Templates.
I will raise an OSS message for this.