I was wondering the same about the platelets in WB. There article addresses it briefly stating "In Pittsburgh, the decision was made to keep WB for up to 14 days in the refrigerator as it was clear from the literature that cold-stored PLT function was well maintained for at least that length of time. Continuous agitation of WB is not recommended as it does not enhance PLT quality and contributes to increased hemolysis during storage. On Day 15 the unused units of WB are returned to the CTS laboratory where the WB is concentrated into an RBC unit by removing the PLT-rich plasma, and the resulting RBC unit can be stored for an additional 6 days."
Not sure what is meant by "the literature", but there are a few cited articles that seem like they may shed some light on this, but I have yet to look at them..
Reddoch KM, Pidcoke HF, Montgomery RK, et al. Hemostatic
function of apheresis platelets stored at 48C and 228C. Shock
2014;41 Suppl 1:54-61.
Nair PM, Pidcoke HF, Cap AP, et al. Effect of cold storage on
shear-induced platelet aggregation and clot strength.
J Trauma Acute Care Surg 2014;77:S88-93.
Becker GA, Tuccelli M, Kunicki T, et al. Studies of platelet concentrates
stored at 22 C and 4 C. Transfusion 1973;13:61-8.
Yazer MH, Glackin EM, Triulzi DJ, et al. The effect of stationary
versus rocked storage of whole blood on red blood cell
damage and platelet function. Transfusion 2016;56:596-
604.