This is sort of a meta-reason, but Northern Australia is a long way from anywhere. Without very many people, it is hard to build a stable agricultural economy. If a bunch of people where sent there and forced to survive, they'd probably eke something out (for example, like the people who first populated Sydney, or South Africa). But since that never happened...population of the reason never happened. Sort of circular reasoning, but without ever having a reason for a lot of people to show up in Northern Australia (prison colony, religious persecution, etc) no one has ever made the infrastructure that successful farming operations could be based off of.
The Australian government agency Commonwealth Scientific and Industrial Research Organisation has concluded that there is "at least 16 million hectares of soil that’s suitable for intensive agriculture".
CSIRO further reports (ibid.) "around 15,000 GL [of water annually]—enough to irrigate almost 1.5 million hectares—could be made available for irrigation" with improved infrastructure.
The Australian government is pursuing modest agricultural expansions. The 2015 White Paper on Developing Northern Australia announced an A$170m allocation for water development in northern Australia, including expanded funding for the Ord River Irrigation Scheme.
Developments must contend with the wishes of local stakeholders and state funding limitations.
Proposals for transformative agricultural developments, including perhaps soil improvement and settlement policies, apparently lack political will. The Kimberley Plan, a WWII-era scheme to resettle Jewish refugees in northern Australia, was vetoed by the Australian government in 1944 on the grounds that it would "depart from the long-established policy in regard to alien settlement in Australia". Immigration remains restricted in Australia, and the government is unlikely to import massive foreign manpower as part of a development scheme. The population and economic pressures within Australia are evidently insufficient to motivate a large-scale development of the north.