I don't really understand this. I get that initiative is good. but there are lot of environments where you could really screw things up if your changing things with communicating. how does the change you introduced get tested? communicated to the customer? how do you know it wasn't a low priority task and had the product owner known there was capacity you couldn't have worked on something higher priority? to me that's the whole point of a backlog and a prioritization process. add it to the backlog and if you have a solution paste the solution into the comments so it can be prioritized.
Hey sharemywin. The key is stepping up and doing things without being asked to do so. The two examples might have over-index on people not asking for permission, but that's not the main message. To be clear, I'm not telling anyone to stop getting buy-in from others or asking for permission.
Process and backlog grooming are effective and necessary, but ownership can also be demonstrated in harmony with process. It could be as simple as flagging a technical area to fix or improve (subject to the prioritization process) instead of only raising issues when asked or saying "this looks broken, I hope someone fixes it" and moving on.