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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. >

True. Although fringe interests can sort of get representation in a two party system, they just have to do it through one of the major parties. Which is admittedly a much harder deal for them that gives them less negotiating power than if they were an actual party with their own leadership.
Both systems involve the formation of a coalition of different groups; a two party system just forms the coalition before the election, and a multi-party system forms the coalition after the election. >


True. Although fringe interests can sort of get representation in a two party system, they just have to do it through one of the major parties. Which is admittedly a much harder deal for them that gives them less negotiating power than if they were an actual party with their own leadership.

Yeah, it can happen to a limited degree, especially in the case of minority interests where the majority doesn't care that much about the issue. In the US there is also the influence of the primary system, which favours the election of extremist/fringe candidates in safe seats, whereas for example in the UK the MPs tend to be party insiders and there is no open primary for the different voting districts.

Both systems involve the formation of a coalition of different groups; a two party system just forms the coalition before the election, and a multi-party system forms the coalition after the election.

That is true to some degree, but the makeup of the coalition is different. Coalitions in multi-party systems tend to be much broader. For example, there have been cases of ruling coalitions with communists and conservatives in them in postwar Europe. This would be hard to imagine in a two-party system, where the parties typically have a single dominant faction. >

True. The effect on the government from fringe groups is moderated; if you're actually a politician, you have to adjust your messaging somewhat to kind of fit into the ideological framework of one of the main parties, even if what you actually care about is your one specific fringe issue.
If 5% of the electorate has their one particular thing they care about under a multiparty system, they just form the This One Particular Thing Party.
Under a two party system, that 5% is probably slightly closer to one of the two major parties, and the type of political activists who would run the TOPTP in another country instead spend their time trying to get that party to make the thing into a slightly bigger part of their platform.
Either way, they won't have a ton of power to influence major changes. But actually having distinct leadership and a name makes negotiation more possible. If your fringe interest has been supporting Main Party A and A screws you over, that might change who's voting for A in the long run. But if most of your politicians already brand themselves as Party A members, you can't respond to that in the same way a minor party dropping support for a coalition could. >


[I]f politics were NOT distributed this way, say it was more like 70:30, then would politics even need to exist in the first place?

Why don't you look at the split between Democrats and Republicans from 1933 to 1970 or so (not that that's the only period in American history where one political party dominated the other). >

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 >

Yeah this is what OP is asking about. Elections are close nationally because parties regroup after losses and re-prioritize or change policies. 
That's why no one is arguing about gay marriage anymore even though it was a central culture war issue in the W Bush years. It became super popular so Republicans don't emphasize being against it anymore. Or why no one is arguing in favor of more Free Trade agreements when NAFTA was negotiated by the HW Bush administration, signed by Clinton.
Longer term, if one party became dominant then it would split in two like the Democratic-Republicans after the Gilded Age. >

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. >

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. >

Paraphrasing the same thing as others. Political parties will adjust their positions to capture as many voters as they can - which in a two party dynamic would be 50/50 >

I'm going to boil this down. In terms of the 537 elected officials in the USA federal government, none of them represent the majority per capita opinions of the country, or the districts they represent.
In state governments, various Republicans (large R) have engaged in widespread election engineering for a number of decades. Those specific state governments no longer represent the per capita population opinions of their state. 
40% of America votes Republican by reflex. 40% of America votes Democratic by reflex. 20% of America changes it's mind a lot, including the feeble minded that voted for both Obama and Trump "because they were different."
And our voter participation is very very low. The more people that vote, the more the democratic party wins. Because popular opinion. >

It is not so much statistics, but strategic political positioning. If there was a 70:30 situation, any candidate who positioned themselves politically closer to the "70" candidate would do better and be thus preferred (it is more complicated than that, but essentially that's how it works). Check out the median voter theorem for a simple case of electoral competition. >

A valid sample ultimately results in a valid extrapolation. A poll properly conducted reflects the popularity of the party and the candidate it represents.  They change over time, in the U.S. by generally enough margins or a few percentage points and that makes all the difference in the U.S. 
If we had multiple viable parties, polls would not be so clear cut, but we are primarily a two-party system, and it shows.