[2] A member of several committees related to finance and technology,[3] Bragg advocates changes to the Australian retirement system[4][5] and supports the 2017 Uluru Statement from the Heart.

He worked to establish two key pieces of industry self-regulation: a superannuation governance standard and the Trowbridge Review & the inaugural Life Insurance Consumer Code of Practice.

[14] Prior to the 2016 federal election, Bragg was an unsuccessful Liberal preselection candidate for both the Senate ticket in New South Wales and the Division of Murray in Victoria.

He was considered the frontrunner for a period, but withdrew from the race due to concerns that the preselection of a male candidate would be poorly received.

[3] He led the effort to create a year-long inquiry into Australia's financial technology sector[17] then chaired the resulting committee.

[19] Bragg led a motion requiring the Australian Broadcasting Corporation (ABC) disclose information about its content-sharing agreement with The New Daily.

[32] He also advocated for big tech companies like Facebook and Google to make a proportional number of content deals with smaller publishers as they do with larger ones.

[33] He participated in negotiations between Facebook and smaller news organizations to broker content agreements with a more diverse range of publishers.

[35] Bragg led the Liberal Party's campaign to support same sex marriage,[36] criticized anti-Asian comments during the COVID-19 pandemic,[37] and advocated for carbon-neutral policies.

[39] He is the author of Fit for Service (2017),[40] the essay "Scrap Iron for Japan" in Paul Ritchie's Forgotten People Updated (2018),[41] and Bad Egg: How to Fix Super (2020).

[42] Bragg also published a book called Buraadja: The Liberal Case for National Reconciliation,[43] a three-part series focused on the history of the rights of Indigenous Australians.