I was ready to put this behind in post #12.

You want to talk facts? Let’s do the math once more because you are ignoring the numbers when they are right in front of your eyes. 113EUR is less than 116EUR. 113EUR is less than 145EUR. Those are product of car rental cost (with fuel) vs. the 29EUR per passenger for 4/5 passengers respectively.

But before I provide references.

You do realize you are arguing from a position of disadvantage and you’re now trying to dig yourself out of the hole you created? What I wrote in post 6 stated a “it depends” position on the train vs. car hire cost. Whereas you are arguing that the absolute position that train will always been cheaper period; end of story.

All I have to do is point out one example of car rental plus fuel being cheaper than the train and that invalidates your argument.

You asked for the facts, so here goes the facts.
Take your 29EUR and multiply by 4 passengers. That’s 116EUR.
Hertz is renting one way Opel Astra SW 83EUR (pick a August Saturday on hertz.co.uk). That leaves 33EUR for gas which I've already establish is enough. Actual gas is closer to 28-30EUR based on experience. Last I checked 83 + 30 = 113 which is less than 116. Doing the math for 5 passengers validates my point even more.

Care to continue to ignore the “facts?”

Your black-white position of trains is always cheaper than the car makes me wonder if you ever even made the DUS to FRA journey at all. Because you're not looking at the real world nor do you fact check.

Delays happen in life. The 29EUR is only good if you jump thru the hoops of booking weeks/months in advance and everything goes according to plan. Where is the passage that states the bahn insurance will reimburse you for a walk-up fare if you have a flight delay? Think about it. If the insurance covers a situation where passenger was late to the ticketed train, no one will every buy a walk up ICE fare. They just do what you are proposing, buy the restricted fare and take the insurance.

The OP indicated he is flying into DUS airport; not flying into city centre. The A44 is right next to the DUS terminal/garage. The DUS regional train station requires a skytrain from the terminal to the station followed by a 2 minute walk to the platform.