Im pretty sure Sangakkara dropped him self the first time around.In Sangakkara's second season he spent more than half the season on the bench. He misfired a few times and the Canes were done with him. The Canes weren't a top of the table side and they could have easily fit him in their side.
Shah played a few seasons and had a poor final season. I remember the commentators were savage on him and the Canes sent him packing before the end of the season.
Point being that particularly in Sanga's case, some players may feel aggrieved by the treatment of their franchise and this may filter across internationally.
Players may not see the BBL as a must play destination.