I found the following comment while searching /r/AskHistorians for precisely this question (for some reason, he has a negative score):
There is little firm evidence on which to date the precise composition of the NT books, except that the few Christian writings surviving from the early second century indicate knowledge of those four gospels and of collections of Pauline epistles. The NT books give almost no clear dates for Jesus himself (Matthew and Luke, as above). Thus their dating mostly reflects scholarly fashion. Whereas earlier fashion dated many of them to the period 100–140 C.E., current fashion puts almost all of them within 50–100 C.E. One leading scholar, John A.T. Robinson, dated them all before 70 C.E., above all because it is difficult to identify any NT author who is clearly aware of the Jewish catastrophe of that year.
What are the main reason that they are placed decades after the events they supposedly describe?
For example, why 70 AD and not 60, 50, 40, even 30?
Well, in the case of the letters that form the bulk of the New Testament, they are written to churches that didn't come into formation until the 40s and 50s, and even mapping them to the chronology in the book of Acts, they mostly belong from the mid/late 50s through to the 70s.
Dating of the gospels depends upon a number of factors. Firstly, the destruction of the temple in 70AD is such a dramatic event in the local area, that the presence or absence of such an event in the texts must be taken into consideration. Secondly, if they appeared very early, you would expect literary usage of the gospels by the letters. Thirdly, you have to give some account of why the gospels were created, and a reasonable explanation fits in with the shift from first generation eye-witnesses to second and third generation churches in which growing formalisation of oral tradition is accompanied by the writing down of more orderly accounts of Jesus. All of which suggests a date no earlier than the 60s.
Does that clarify why they are rarely dated 'very early' in the 30-60AD period?