High-latitude (\b\ > 30°) molecular clouds have virial parameters that exceed 1, but whether these clouds can form stars has not been studied systematically. Using JCMT SCUBA-2 archival data, we surveyed 70 fields that target high-latitude Planck Galactic cold clumps (HLPCs) to find dense cores with density of 105-106 cm-3 and size of <0.1 pc. The sample benefits from both the representativeness of the parent sample and its coverage of the densest clumps at the high column density end (>1 × 1021 cm-2). At an average rms of 15mJybeam-1, we detected Galactic dense cores in only one field, G6.04+36.77 (L183) while also identifying 12 extragalactic objects and two young stellar objects. Compared to the low-latitude clumps, dense cores are scarce in HLPCs. With synthetic observations, the densities of cores are constrained to be nc ≲ 105 cm-3 should they exist in HLPCs. Low-latitude clumps, Taurus clumps, and HLPCs form a sequence where a higher virial parameter corresponds to a lower dense-core detection rate. If HLPCs were affected by the Local Bubble, the scarcity should favor turbulence-inhibited rather than supernova-driven star formation. Studies of the formation mechanism of the L183 molecular cloud are warranted.