The Norman door has been working for plenty of years, and it will keep on working. Figuring out how to push or pull a door open isn't difficult. Even if you guess wrong the first time, you've only wasted a second or two. People need to stop thinking everything in life has to be quick and easy.
There is a reason for everything. I am sure the reason for these doors is that they can all be manufactured one way and put on whatever entryway in whatever position needed. Sometimes cost and manufacturing trump usability. Many doors of this kind will swing either way.
Many also have a push plate mounted on the handle.
A door that requires an instruction manual to use is poorly designed. A very simple and straight forward alternative already exists. A flat plate on one side prompting you to push, and a handle on the other side prompting to pull makes much more sense. One of the reasons on the 'Yes' side argues "sometimes costs and manufacturing trump usability". A small flat plate as opposed to a second handle is not only lighter (and therefore cheaper) but much more straight forward to fabricate and much more compact, therefore easier to store and transport.
We need to see and understand the past to build on our mistakes. With designs, it's sort of the same. Norman doors are confusing and can cause accidents or injuries. Mostly the design signals can conflict with printed push/pull instructions. If we can do better, why shouldn't we replace poorly designed doors with better ones?
Poor designs, like the Norman door, need to be phased out in favor of better ideas. These kinds of ideas are still in use because they are what we have become used to, but as better ideas and designs become available we need to adopt them so we can live better lives.