@Ciell I don't think that is changeable. If you want to use a template, you should be using the template inserter, not the references list inserter. On en.wp we have made the layout of <references /> equal to the layout of {{reflist}}.
And using it like that, will also make the params of the template unreachable, see usages of {{Reflist}} inside of english wikipedia. Because it sees the references element inside of the template, it knows that it will have to live update that content (based on refs beings added/removed etc), and other changes are for that reason not possible.
Of course, you can manipulate the Toolbar using Javascript to do whatever you want. But that is up to the communities that want to deviate from standards.