Halliday & Matthiessen (2014: 585):
It is in this area that expansion and projection come to meet and overlap. Causing something to be done means that it is done, with ‘external agency’ as a circumstantial feature. Wanting something to be done means that it is envisaged, or projected, but may or may not happen: its status is that of a metaphenomenon, not a phenomenon. But the line between the two is fuzzy. In general, if the relationship can be expressed by a finite that clause, as in she wished that he would come, then in principle it is a projection; but in this respect too there is a ‘grey’ area: she wanted that he should come is possible, but uncommon, whereas she allowed that he should come is uncommon, but possible.