1. Crosstrek costs more ($22,145 vs $18,695)
2. Crosstrek is less efficient (33/27 mpg vs 36/28 mpg)
3. Crosstrek is taller (64" vs 59")
4. Crosstrek outsells the Impreza in the US (131k vs 66k)
Americans love feeling tall and are willing to pay for the extra few inches.
The Crosstrek also gets a beefier rear diff, stiffer suspension, and larger brakes too.
They're the same platform, and share a lot of bodywork, but that's not uncommon among manufacturers now. The Golf and Atlas are both on VW's MQB platform now but that's about where the comparisons end.
"The Crosstrek also has a beefed up locking center differential for towing and a standard six-speed manual transmission,The Impreza’s manual only has five gears..."
https://cars.usnews.com/cars-trucks/impreza-vs-crosstrek
That certainly accounts for the price difference. Those higher end parts have real costs. And, Americans have plenty of stuff to tow around. (I am an American car guy.)
As you probably know, it's beneficial both for the wide opening to insert larger objects into the trunk as well as the folding of seats (less common in sedans/saloon cars) to provide much more space when rear seats aren't needed.
The Crosstrek comes stock with a 6-speed manual instead of the Impreza's 5-speed (though 90% of them are sold with the execrable CVT instead); the Crosstrek only comes as a hatchback while the base Impreza is a sedan; the Crosstrek has intermittently been available with a hybrid system.
Though I think the idea that the more expensive model is pushed by dealers makes sense too.