I'm not sure I understand why you can't just use 'skriver' here?
because 'skriver' is in the present tense.
Because you have to use the infinitive form of the word, like in English. In English it's: "to write" and so it should be "at skrive" in Danish.
The normal version of the audio is WAY off sounds like "VI tager tid at skrive en hel bog," while the slowed down version is correct.
So it's literally the same as in English ("it takes time")? Can any native approve?
Not a native, but I know from experience that it is exactly the same as in English.