I recall hearing that as the reason for no images of the screens in the SpaceX spacecraft. The controls and data on the screen was considered a trade secret and so was not to be shown to the public as that might give data helpful to SpaceX competitors. I expect that there is plenty of data on the screens at a mission control center with this same kind of data on the screens, and applies to trade secrets to any spacecraft made by anyone.
What we get from the broadcast of these missions will be things that they cannot hide from the public. A rocket launch will make a lot of noise, put a very bright object into the air, and therefore can be tracked with great precision by anyone that wants to bother doing so. Spacecraft manufacturers might prefer people not know how fast and how high their rockets can go but there's no hiding that.
On some of those screens will be the telemetry from health and safety sensors on the crew, that's medical data that might be protected under law.
Something that lands on Mars will likely be tracked by foreign nations as there's a number of nations with their own satellites orbiting the planet and making observations. There's not going to be any trade secret or national security implications on giving away where something lands on Mars.
NASA is a federal government agency and will use resources from other space capable federal agencies in tracking anything launched into space. Space Force assets could be in use and giving away names and places on a screen might have national security implications and therefore will not be shared with the public.
Because it will be difficult to separate what can and can not be shared in real time it's simply going to be easier to not allow any screens to be shown. NASA will control this flow of information and mundane details they are willing to share will be put on large screens for people on site and streamed over the internet.
Trade secrets does appear to be the biggest reason to not allow people to see the computer screens at NASA.