Some major differences between the Commonwealth-country parliamentary system and the US's system:

1. The US constitution originally ratified in 1789 was not designed in anticipation of the emergence of rival political parties, or the "factions" that Washington warned about close to his death in the late 1790s. The parliamentary system first developed in the UK, especially post-Peterloo, has a specific system built in to allow multiple parties with sufficient ideological/policy overlap, none of which enjoy majority representation by themselves, to form a majority coalition. The US system's first-past-the-post/majoritarian method for deciding elections, in combination with a starker separation of executive/diplomatic power from legislative power, one which divides the roles of a prime minister into the roles of house speaker and president. It's also worth noting that the US's equivalent to a House of Lords, the Senate, is still significantly more powerful than the House while the longer 6-year term period for senators means a bad senator can't be so easily recalled either through the regular election process.

2. There is no such expectation among US representatives and senators that members of a party must vote alongside the party line. "Maverick" senators such as Joe Manchin are not usually subjected to harsh internal party discipline or threatened with expulsion or recall for consistently voting against the party line, unless they consistently vote in opposition to the interests of capital. House members are more likely to be "primaried" as punishment for deviation but all voters in their district ultimately decide whether this de-facto recalling happens, rather than party membership.

3. The major US parties, the Democratic and Republican Parties, aren't really political parties in the conventional sense. Voters registered to vote Dem or GOP aren't members of those parties. Common partisan voters don't pay dues to the parties they vote for, and most don't attend local or state-level party meetings and enjoy the same sort of internal mass democracy one might expect to see inside, for example, the UK's Labour Party. True membership in either of these parties, if such a thing exists, is limited to high-ranking party bureaucrats (at the state level if not the federal level), almost always upper-middle class if not members of the ruling billionaire class who give or receive millions in donations to party candidates or to the party itself. These two ruling parties have are functionally private organizations, and leading Democrats have openly admitted such to be true for the Democratic Party - that they reserve the right to choose their candidates if they wish. This is why there appears to be not much more than the flimsy pretense of internal democracy in party primaries.

4. Furthermore, the Democrats (and to a lesser extent the Republicans) aren't bound to follow their national party's program, or as they call them here in Yankeeland+Dixiestan, their "political platform", as implied in point 2. These platforms are decided at the quadrennial convention held after the conclusion of a presidential party primary, usually a consensus centered around the stated (though often not actual) policy goals of the primary's victor, with some nominal non-binding concessions to popular losers (e.g. Bernie). On a more local scale, Republicans in states dominated by Democrats are allowed to pursue policies further left than you'd expect their national party to allow in a Parliamentarian system, which is is why we see Republican Massachusetts governors like Charlie Baker who are nigh-indistinguishable from the likes of Biden or Cuomo. Furthermore the same is true - even more true! - for the openly right-wing and milquetoast Democrats in GOP-controlled territory who often take positions against those of national Democrat voters in order to win their local elections (Beto; whichever loser they ran against McConnell in 2020; not to mention Joe Manchin himself).

5. The national parties are much more decentralized, functionally federations of state parties bearing the same party banner. This is because national elections (usually presidential ones) are decided by state elections, taking more on the federal character of something like an EU parliamentary election than the national elections held in the UK or Commonwealth states. This is a vestigial consequence of the early late-18th/early-19th-century conception of the US as an EU-like federation of multiple semi-autonomous ex-colonial states. The state election system is specifically designed to ratfuck smaller 3rd parties with internally-democratic membership and structures (Greens, PSL for example, as we saw last year), forcibly divorcing the legitimate primary system from the internal democracy of a corresponding party precisely because of the duplicitous character of the Democratic and Republican parties. Being registered as a Green voter on a state election commission allows you to vote in a Green primary but is functionally independent from whether you're actually a member of the Green Party for the same reason this artificial separation exists between registered Dem/GOP voters and actual Dem/GOP party members.

TL;DR: there is so much more working against internal democracy (or even internal coherence) within the national "parties" in charge of the US. The US system is a clusterfuck compared to the Westminster-style party system, whose net result is almost invariably the diffusion of accountability that keeps the heat off party leaders. The entire US system has multiple layers of obfuscating bullshit like this that makes it really hard for regular voters who aren't rooting for Team Blue or for Team Red to figure out who's to blame for policy failures in the routine partisan and factional shitstorms resulting from regular finger-pointing and scapegoating.

In Soviet China even the politicians must bow to the Party Line