I'd attribute that to the fact that New Jersey likely didn't have a great supply of goal scorers to supply the OT heroics.
In the first chunk of Brodeur's career, the Devils were above average offensively (and top notch in a few years). But they still went 6-12 in OT from 1994-2001:
94: (1-4) 2nd in GF
95: (2-1) 13th
96: N/A
97: (0-2) 16th
98: (0-2) 9th, both losses against Ottawa who was 24th out of 26 teams in offense
99: (0-1) 2nd
00: (1-1) 2nd
01: (2-1) 1st
I suppose you could make the argument that the Devils were offense by committee, so when teams shortened their benches then perhaps they were at a slight disadvantage in a one game sample. But then Brodeur went 10-12 the rest of his career when the Devils were below average offensively, so that's a bit odd as well.