What I'd love to see, is to be able to assign one person as the one "responsible" and then assign others ad-hoc when/if they work on-, review-, discuss, or co-author it.
Some software allows multiple assignees, but as the ancient management-saying goes: if everyone is responsible, no-one is. So i'd still love to have one person assigned with a special role or label.
My previous company used Phabricator and you only assigned yourself a task when you actually started working on it. It meant anyone could work on anything - much more agile and much much better knowledge spreading and teamwork.
But I understand where my current company is coming from. You want a "person who is responsible for making sure this eventually gets done" field and a "person who is currently working on this" field.
Indeed. But the last part should be plural. Because in reality multiple people work on it. A reviewer, someone who helped with the UX, the person you spoke to to get the exact business-details right, that colleague you needed to finetune the SQL, or the moment bob goes on vacation and you need to step in and take over his work.
So each ticket gets a Primary Developer, Primary SME, etc, but might get assigned to some one else to do one small bit of work (e.g., it'll get assigned to a different developer for code review, but whoever's listed as the Primary Developer is still responsible for it).