I appreciate sharing it with your team. On the topic of getting updates from contracts, I've had a similar (frustrating) experience. One thing we offer to make that easier is a Slack integration to proactively alert the relevant stakeholders when an important event has happened with a contract. We also have an API and webhook for getting it into other systems.

For internal legal teams, the biggest motivator is often re-allocating their time to more strategic and/or more interesting work. They have a long list of other projects that they'd rather focus on if they can reduce their time spent on yet another NDA or routine sales contract.