Kozuka landed his only successful quad in competion. He had nothing to lose and no pressure on him at that point, being at 6th but just having the door wide open with Dai and Nobu having screwed up. He was able to land a beautiful quad and perform a flawless program.
From my perspective, I thought the pressure on Kozuka was tremendous. Japan, at that point, was about to be shut out of the podium after the mishaps on the part of Oda and Takahashi. The Japanese fans in the arena were visibly nervous and unsettled, almost sound like they were desperate for Kozuka to deliver. I think Kozuka knew exactly what he had to do and letting the country down was not an option - he is after all, the current Japanese National Champion.
What lowered his TES BV was landing his 3 Loops poorly near the end of the program, missing out on the 3T. He had the presence of mind to tack a 2T to the subsequent 2A but missed some BV as well as GOE points. His BV and total TES were much higher at Nationals, which were not out of line relative to his GPF and Worlds scores.
No, that's not correct. Landing his 3Lp poorly didn't affect his BV, only the GOE since it was neither < or <<. At that point, he had no more space for any Triple jump seeing that 3T was already done with the 4T combo and two jumps of 3 revolutions and higher were already repeated (4T and 3Lz). Skater may not repeat more than twice a jump of 3 revolutions or higher. He never intended to do a 3T after the 3Lo - if he did, he would have suffer the same fate as Oda's 3A+3T combo. His total BV is actually largely the same as the Canadian Nationals. His plan was to have a 3Lo+2T combo, which was switched to 2A+2T instead. Where he actually lost ground is in the GOE, hence a lower TES total overall. In fact, if you recall, at the Cup of Russia 2010 in the exact same arena, he committed an Oda-like error by adding a 3T behind his 2A and resulted in the 2A being voided, thus handing Verner the victory.