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I think it has more to do with the two party system. If we had a parliamentary proportional system, then different groups would need to make coalitions and there would likely be more bipartisanship. As it is now, the extremists can hijack a party and force the rest of the members to follow along.
The 50/50 split is not a matter of statistics but of sociology, and is a feature of two-party systems. In such a system, it is a bad idea to focus on issues that have support from only a tiny minority, because the opponent will pounce and easily capitalize and take the much more popular position. So in a two-party system, political discourse is often dominated by wedge issues over which the populace is divided roughly 50/50. You can see this in other two-party systems as well, such as Brexit in the UK during the previous general election. Wedge issues shift over time: the Republicans in the US have moved away from homophobia as the acceptance of homosexuals has steadily increased, and shifted towards transphobia.
The dynamics is very different in multi-party systems. In such a system, it can be beneficial to focus on minority issues and interests, if there is a small group with strongly held beliefs. For example, in the Dutch national parliament there is a party that supports a literalist interpretation of the Bible, including support of the death penalty (which is banned in the EU), even though only 10-20% of the population regularly attends religious service. There is also a party focusing on animal rights, and an openly anti-Semitic anti-immigrant party. In a two-party system, such fringe movements would not survive. >

Go back further in history. Or to other elections that aren't nationwide. There are plenty of landslides, and politics still existed where and when that happened. >

If one side had a huge majority, they would likely begin doing things that tested their popularity. The minority party would also adapt to hold more popular positions