Unlike the usual belief that the access to the 2nd stability regime of the H-mode pedestal is facilitated by strong plasma shaping, high triangularity is shown to induce a local breakdown of the access by destabilizing the ideal or infinite-n ballooning mode in the outer-well region, where n is the toroidal mode number. This destabilization in high triangularity regime is conjectured mainly due to the substantial increase of the magnetic shear, which can then make the stabilizing magnetic well effect sub-dominant. A large similarity observed in the mode excitation condition and location suggests that these locally-destabilized modes may be a possible source of the broadband fluctuations which are believed to trigger the wide pedestal quiescent-H (QH) mode in low toroidal rotation limit.