Re: The boss is correct, Canada is very different.
"At the federal level Canada has three main branches of government. The Court, the Senate, and the House. Of those two of them are filled by appointment. Almost all key positions of power are by appointment and the House, the only branch with elected members is controlled by party rule."
What a simplistic, blinkered view you have on this matter.
Almost all governments are at some level controlled by appointments and indirect forms of democracy. In Canada, senators are appointed by the government of the day, and serve until age 75 or voluntary retirement. This does build in some 'time lag' and smooths out election to election variation. Looking at anomalous election results, often unexpected by anyone, in some countries, the idea of having a bit of stability while reconsidering what you have done and evaluating a new government seems to me to have some merit.
In the UK, for example, the House of Lords is a mix of hereditary aristocrats (!!!) and life peers, appointed, ultimately by the government of the day. Unlike the Canadian Senate, the Lords appear to have a more accepted role in originating legislation, rather than providing a second opinion, and it seems the peers are found in the British cabinet, whereas in Canada, cabinet is drawn from members of the elected House of Commons. Furthermore, it seems that the British system of 'whipping' is more overtly coercive in forcing party discipline on MPs. British judges are, of course, appointed.
In the US, there are effectively only two parties, and the structure is such that there is no credible chance of a third party becoming significant. That means the two of them can cozy up in one really close ideological and policy position, and there is no mitigating effect by a third party providing a real difference that can drive a broadening of the political spectrum. Furthermore the whole structure of registered party memberships and primarys gives the political 'elite' control over the ability to run, again empowered by limitations of the two party system. The US president is appointed by the Electoral college under a non-uniform mix of rules decided on by 50 individual states, and many of them are under no obligation to pay any attention to the desires of the people electing them. Higher level US judges, at least federally, are appointed. Lower level/local judges can be elected (!!!) possibly one of the worst ideas for a justice system ever invented.
In Australia, the rules allow so much political infighting that they have revolving Prime Ministers, and choice of prime minister is by the MPs, without much constraint from public will... certainly many of them become Prime Minister without standing for election as party leader, thus giving the people some input in this matter.
In many countries with proportional voting, who gets elected is to a large extent controlled by the parties, who decide what order people appear in the party lists. If you are at the top, you are probably in. If you are at the bottom, you are out, and the electorate cannot, mathematically save you. Then the deal-making to create a coalition large enough to govern begins, and the government is determined by negotiations among the favourites of various parties. Studies of the mathematics of such systems show disproportionate influence on policy by third and fourth largest parties as they make deals with large parties desperate to form the government. For an similar situation in a first past the post electoral system, look at the influence of the DUP compared to its percentage of MPs in the British House of Commons.
Parliaments with many parties have not only the corrupting influence of coalition pandering to minority parties but also instability and large delays in forming governments. Look at Sweden, Germany, or Italy for some of the problems.
No system is perfect, but on the balance the Canadian system seems to work fairly well, with some distortion due to Quebec privileges.