Australia's political parties, with the notable exception of the Australian Democrats are famously closed institutions with most powers exercised by the party leader or (occasionally) the caucus. Our political parties are also suffering dramatic declines in membership and participation. Opening them up with a system of primaries would do a lot to cure that problem. Canadians take the principle of party democracy so seriously that there are proposals to enshrine it in law. For instance in New Brunswick, the Commission on Legislative Democracy recommended this amendment to the province's electoral act.
2.1 All of a party’s general election candidates must be endorsed by a vote of eligible party members, in a vote that is open to all eligible party members.
2.2 To be eligible for party membership, a person must meet the same eligibility requirements to vote in a provincial election.
2.3 To be eligible to vote in a leadership or nomination contest, a person must belong to the political party at least seven days prior to the nomination contest and be a member of the party at the time of the vote.
2.4 If fixed election dates are adopted, riding associations must hold a vote of their members for the purpose of choosing their general election candidate no more than 120 days prior to the date of the general election.
2.5 Parties must advertise the date, time and location of a leadership or nomination contest at least seven days prior to the closing date for eligible membership.
2.6 Parties shall not charge a membership fee greater than $5 annually.
I have problems with both conventions and exhaustive ballots. In Australia, if we ever got this far, I suspect we'd go for a direct vote and use preferential voting. The electoral commission runs union elections. There's no obvious reason they cannot run party elections just as well.