Time to pickup rental car is going to be about the same as getting the train. The DUS car rental garage is physically closer than the DUS regional train station. The entrance to the autobahn is only a right turn follow by a left turn out of the garage. If you've driven enough, you would know that effect additional petrol between one and five is minimal (the bulk of the mass is the vehicle itself). Even if you factor in a generous 10% extra fuel, it still cost less than the walk-up fare of the train (depending on party size).

As for travel insurance, you're just randomly throwing out ideas without even looking at them in detail. The bahn insurance will cover the discounted ticket if passenger happened to be dead or suffered a serious illness. It doesn't covert flight delays.

Time is money. If the extra time waiting for the train is not factored in, then traffic jams should not be in your argument against auto either. I’ve done the drive 2:15 to 3 hours (without/with summer construction traffic).

I see the 29EUR non-stop in August. So I'm update my statement to reflect.
Is the train always going to be cheaper than car rental? No.
Is the train a fractional cost when travelling with a small party size and booked weeks/months in advance and everything goes according to plan? Yes.
Is the train a fractional cost when travelling with several passengers or if you to miss the reserved discounted train? No. The train might be comparable (again depends on the number of passengers) but it could also be significantly more expensive especially if you miss the ticketed train while on a Sparpreis fare.