BRE,
this is, for me, indeed one of the crucial aspects (or holes in the Swiss cheese):
"After the aborted approach to Hamburg and their entry into the LUB Lübeck holding pattern, the next task was to reach a decision upon how the flight should continue. If there could be no landing at the original declared destination, a diversion to a predetermined alternate airport is a standard operating procedure. Because Bremen was behind the weather front and the crew was not prepared to penetrate the front or fly around the frontal area, the decision to divert to the second alternate – Hannover, which by that time was also behind the cold front – is not understandable." (BFU, p. 39)
After this initial and maybe flawed decision (and I use "flawed" with extreme caution here as I am not in a position whatsoever to make judgements), and once on their way to Berlin, we have to consider this:
"At this time, their weather radar indicated that the Berlin area seen in their screen was as yet unaffected by the approaching front, and requested an approach to Berlin-Tegel. At this time, no further options were discussed. The controller gave clearance for the flight to Berlin-Tegel.
At 2015 hrs the crew monitored the ATIS broadcast for Berlin Tegel; this supported their decision of two minutes earlier to divert to Berlin Tegel. Information Delta timed at 1950 hrs gave the impression that the prevailing weather at the airport was very good (CAVOK). The NOSIG Trend suggested that the weather conditions were stable. The BFU holds the view that the crew’s estimate was understandable." (p. 37)
I find that last remark crucial. Once they had made the decision to head for Berlin they were supported in their view that this was the right, and appropriate, choice, rather than look for, quote BRE, littered "aerodromes that can handle a regional airliner". Understandable. (?)