Whatever is needed goes into commit message and referencing tickets in separate system is a feature not a bug - because JIRA or any other system is used to communicate with non developers. Like business analysts don't get access to code or repositories at all for example or support people don't get access to the repositories and code.
Yeah I can see how one could write front end to get the notes visible/editable by non developers but it still does not make any sense because BA/Support others don't care about specific commits and a single feature might fit into a commit but most likely does not. Even more fun is when you have multi repo and your feature touches couple services then git notes are quite useless because then you really need reference to outside system.