"despite great efforts" is a correct and commonly used phrase in written English.
It is typically used to express a contrast or contradiction between the efforts made to achieve something and the actual outcome. Example: Despite great efforts to reach a peaceful resolution, the conflict between the two countries continued to escalate.
Despite great efforts, primary and secondary education everywhere retained certain traditional features.
And despite great efforts to bring in black-owned companies, the JSE remains almost exclusively white.
Despite great efforts, it has attracted derisory attention from beyond the professional development world.
Despite great efforts to improve schools and universities, workers in the emerging world are less educated than those elsewhere.
And on the fact that, in Nigeria, the disease is continuing to spread despite great efforts undertaken by the government.
Despite great efforts to implement retrofit techniques in Sweden, no stringent evaluation of the benefits of these techniques or their systematic design has been completed.
It was, though, a revelatory moment: one last cry of frustration from an administration that, despite great effort, and persistent lashings from Vice President Dick Cheney, has been largely unsuccessful in undoing three decades of environmental law.
Despite great effort in the antiviral drug development and vaccination research fields, viruses are still major threats to public health.
But despite great effort, the educational system as a whole has been unable to apply this truth on a broad scale, to produce better results, until now.
It's no secret that innovation is tough to pull off, and even the "most innovative" companies, such as General Electric (No. 18 on Boston Consulting Groups' most recent list) and Whirlpool (tariffs aside, consumers favor Korean and European styling and brands) and Proctor & Gamble (sinking to No. 47 on BCG's list) can fall fast, despite great effort on the part of their innovation leaders.
