Say for example I want to use Touch Bar for time tracking, or todo list application. It'd be super useful to have something that's always there no matter which application I'm viewing.
The Touch Bar is not meant to show background and/or system wide notifications.
Apple has put out a document called macOS Human Interface Guidelines which is intended to communicate to developers how UI elements should be implemented; there's a section specifically about how the touch bar should function.
Under the Design for the Touch Bar Section, it provides guidelines as to how the Touch Bar should be utilized within the context of an App.
Design a contextual experience. Make the Touch Bar relevant to the current context on the main screen. Identify the different contexts within your app, and consider how you can expose varying levels of functionality based on how your app is used.
And more specifically to your question, because "background/system wide applications" would provide notifications and it's UI and to the screen (via Notifications most likely), not through the keyboard:
Use the Touch Bar as an extension of the keyboard and trackpad, not as a display. Although technically it’s a screen, the Touch Bar functions as an input device, not a secondary display. The user may glance at the Touch Bar to locate or use a control, but their primary focus is the main screen. The Touch Bar shouldn’t display alerts, messages, scrolling content, static content, or anything else that commands the user’s attention or distracts from their work on the main screen.
Apple's developer API reference for NSTouchBar explicitly states how the contents of the Touch Bar are determined (emphasis mine):
On supported MacBook Pro models, the Touch Bar, above the keyboard, shows instances of the NSTouchBar class from the front-most app.
macOS itself regulates what is shown on the Touch Bar at what time, and as noted above, this changes when the front-most app does.