Arguably there are no big cities in Denmark at all. Looking for lists of populations of "big cities" across the world I can't even find one that includes Copenhagen to make a comparison of just how far down the list it is.
In any case this is all just silly nonsense. The reason people don't prefer the train vs. almost every other mode of transportation is because its extremely expensive. Making it faster isn't going to solve the root problem. But of cause just like everything else in government, the main aim of the future is to build up huge infrastructure projects with individual companies who stand to gain billions... and just so happen to have some senior exec positions open for the politicians running the sham.
If they'd taken the money they would have spent on this large project and instead just lowered fares, that would be an overall much better reality, but then no individual company is making billions and there's no promise of that sweet executive position.