Why doesn't this reaction happen?
This elimination is unfavorable because C--C bonds are generally quite stable. Decarboxylation would involve the formation of an unstable carbanion before proceeding to the elimination as you have outlined. (Note, this is more favorable under different functional group conditions, namely when a neighboring carbonyl can stabilize the carbanion through the formation of an enol  https://www.masterorganicchemistry.com/tips/decarboxylation/ ) So, the formation of the alkyne is favored here over the elimination of CO2.