Why can't we oxidise allylic alcohol to aldehyde using pyridinium chlorochromate?
There are indeed examples of $\mathrm{PCC}$ oxidation of allylic alcohols to $\alpha, \beta$-unsaturated aldehydes. The first example is from the original Corey-Suggs paper while the other two cases are from the work of Dauben and Michno.


References:


E. J. Corey, J. William Suggs, “Pyridinium chlorochromate. An efficient reagent for oxidation of primary and secondary alcohols to carbonyl compounds,” Tetrahedron Letters 1975, 16(31), 2647-2650 (https://doi.org/10.1016/S0040-4039(00)75204-X).
William G. Dauben, Drake M. Michno, “Direct oxidation of tertiary allylic alcohols. A simple and effective method for alkylative carbonyl transposition,” J. Org. Chem. 1977, 42(4), 682–685 (https://doi.org/10.1021/jo00424a023).