I think the answer is it depends on what job functions you want your publisher to do.
In terms of feature services:
If your publisher needs to do call processing then the Call Manager service needs to be running. If the pub is not doing call processing it can be off.
If you want your pub to be a tftp server as well then you need the tftp service running. If not then it can be shut off.
If you want to use the DNA tool then you should have Cisco Dialed Number Analyzer Server and Cisco Dialed Number Analyzer running, if not that it can be off.
If you plan on using TAPS then you should have the Cisco TAPS Service running, if not then it can be off.
For network services similar logic applies:
If you want to backup and restore capabilities then you need Cisco DRF Local and Cisco DRF Master up and running.
I think the use of the word mandatory is open to interpretation here.
For example its not mandatory for Tomcat to be running on your pub. It wont prevent phones from registering to the sub's and prevent them from taking calls. However if its not running then you cant login to your publisher and make changes.
Its not mandatory for DRF services to be running either for the phones to work but then you wont have backup and restore capabilities working.
So I think the key here is to fully understand your environment and requirements and act accordingly. Having a good understanding of what each service is and does will be helpful.
You can find a detailed list of services and what they do in the Serviceability guide found here
https://www.cisco.com/c/en/us/td/docs/voice_ip_comm/cucm/admin/12_5_1/admin/cucm_b_serviceability-admin-guide-1251/cucm_b_serviceability-admin-guide-1251_chapter_0101.html
