Static fixed displays are strictly superior here. In an emergency situation, the last thing you want, is to look down at the computer, and see a new unfamiliar display layout. It adds cognitive load at the precise worst moment to do so.
That said, I do think big improvements in these displays are possible, but mostly through better organization and font size choices.
Not sure if I am following you - progressive information discovery (aka "progressive disclosure") is one of the key concepts of good interface design. You show only the basic information first and let users see more info if necessary. A typical example is "basic" vs "advanced" settings in software. "Normal" working mode and "emergency" modes will be different here - "contextual awareness" in ux design. For example, if my battery is good but I need to pay attention to the cells during an emergency, why should I see battery info on the screen? I.e. a well-designed interface will focus users only on the information required for the user to perform a specific task in the given context. Approachability wins here.
As for your question, there are at least two things that stop you from seeing unfamiliar display layouts.
First, tutorials. Yes, users will have to read just like they do now.
Second, baked in emergency scenarios. It is possible to show emergency situation simulations. You don't have to do this in the actual hardware/dive computer - an phone app or a web site is sufficient. Integrations with different manufacturers will add substantial costs in this as the company making a dive computer will have to understand what emergency situations may happen in various CCRs and then account for those scenarios.
In general, good user experiences revolve around understanding the jobs that users must do while using a product. For a CCR diver, we can define the following jobs:
1. Get a unit ready for a dive.
2. Monitor the unit during the dive.
3. Change settings during the dive.
4. Deal with emergencies.
5. Perform post-dive configuration.
Each of these jobs may have sub-tasks. Unfortunately, many of these jobs/tasks will be unit dependent which means additional costs for all the parties involved. That's why Shearwater does what it does. Some screens are static and are open to use interpretation (e.g., showing PPO2 for individual cells.) Other screens correspond to the general flows applicable to divers on all units (e.g., define gas).