You can simply do this by using the transform tool while holding 'command' for a mac. This allows you to drag the corners of a shape individually, effectively the same function as the free distort tool in illustrator.
I think you don’t understand the issue.
It’s not Illustrator’s inferior transformation behaviour that is desired in Photoshop but Photoshop’s Free Transform behaviour that is being desired for Illustrator.
Illustrator’s »Free Distort« is, in my opinion, close to useless because of the lacking preview or integration.