Why did the Beechcraft Starship use a delta wing?
Because it was something of a Burt Rutan trademark since his early days. His first designs, the VariViggen and VariEze, had such a wing already, and apparently he saw no reason to optimize the wing of the Starship.



Rutan VariEze in flight (picture source)

The only true innovation was a variable geometry canard, which he even patented. Being only 85% scale, the performance of the Starship prototype was formidable, but once the real production aircraft had been designed with full compliance to airworthiness regulations, the Beech Starship turned out to be less impressive. The additional wetted surface produced more friction drag. Piaggio's design is clearly superior.

By the way, the idea behind the variable geometry canard was sound: In the landing configuration it would balance the additional lift from the fowler flaps on the wing. But the whole mechanism cost more in weight than the reduction in drag during cruise could save.



Drawing from US Patent 4641800.