The projectivity restriction itself has not been linguistically motivated to date.
an efficient exact algorithm for this restriction would pose a starting point for various relaxations of the definition (also known as mild non-projectivity) that reflect linguistic description of the data, as has been done for the Eisner algorithm (in for example (Bodirsky et al., 2005;Gómez-Rodríguez et al., 2011;Pitler et al., 2012;Pitler et al., 2013;Satta and Kuhlmann, 2013)).