In the reaction of propyne with $\ce{HBr}$ this cation (prop-1-en-2-ylium) was mentioned by my teacher: $$\ce{H3C-\overset{+}{C}=CH2}$$

He told me that the carbocation will not rearrange as it will have no change in stability. When I pointed out that the carbocation could shift away from the double bond, as this will provide resonance stability to the carbocation, he just got silent for two minutes and then said it does not rearrange.

Can someone please explain why it cannot rearrange?