Telling a company "The government says you have to patch and is offering to do it for you" seems like it might not go over quite as well as you might hope. I can already see the first thought - "Do they actually care if all my systems work the way I need them to afterwards?". Having worked in Information Security and offered to fix things for people, my experience is that entities going for this is extremely rare, even when it's just the next department over.
As for the NSA, well, getting them into a proactive posture is a wonderful idea! It's such a good idea that the US government decided you were right decades ago. And acted accordingly. This tends not to make the news, so many people are understandably ignorant. For example, the NSA publishes information assurance best practices: https://apps.nsa.gov/iaarchive/library/ia-guidance/ia-standa...