The republic versus democracy point is relevant here for a practical reason, not an ideological one. In a direct democracy, citizens can vote on each issue independently of the others. In a republic, they have to pick representatives that don’t necessarily have the exact same mix of preferences, and those representatives are organized into parties. That produces compromises that don’t need to happen in a direct democracy. For example, a major cleavage line in American politics is race. That splits the working class vote between Democrats and Republicans. And it also splits the religious conservative vote. For example, likely voters support the Hyde Amendment (which bans federal funding of abortions) by a 20-point margin: https://slate.com/news-and-politics/2019/06/joe-biden-hyde-a.... But Joe Biden now supports federal funding of abortions. Thats because the social conservative block is split between the two parties. Conservative Hispanic and especially Black people often vote Democrat for other reasons. In a referendum, federal funding of abortion would be easily defeated. But in a system of representative government, it could become law.
Many other issues split this way. Over 60% of people support eliminating qualified immunity (which shields police from lawsuits) and limiting police union power. In a direct democracy, these issues would win easily. But support for these policies is split between the two parties. Moreover, the parties vigorously disagree about how city mayors handled the protests and riots this summer. So discrete issues like these where there might be bipartisan agreement get sucked up into a larger ideological dispute about when violent protests are justified in reaction to police brutality.
1) You'd be surprised by what people want. As a background principle, Americans don't like government and don't like government regulation: https://news.gallup.com/poll/243662/americans-worry-less-gov.... The percentage of people who want more regulation "of business and industry" hovers around 25%. Even during most of the George W. Bush presidency, those who wanted less regulation substantially outnumbered those who wanted more. Folks who wanted less regulation outnumbered those who wanted more 2:1 in Obama's first term.
The percentage of people saying the federal government has "too little power" has been under 10% over the last 20 years. Since 2005, a majority has said the federal government has too much power.
2) People might want something in the abstract, but that doesn't mean they support a specific implementation with specific trade-offs.
As of 2007, a majority of Americans said they wanted government to guarantee healthcare: https://www.nytimes.com/2007/03/02/washington/02poll.html. but look at the question more carefully: "Americans showed a striking willingness in the poll to make tradeoffs to guarantee health insurance for all, including paying as much as $500 more in taxes a year and forgoing future tax cuts." $500 is just 1.5% of the median individual income. That's not nearly enough to actually pay for European-style universal healthcare.
Unsurprisingly, support for the Affordable Care Act started out well under 40%: https://www.wsj.com/articles/recent-warmth-toward-affordable.... Opposition to the law didn't outweigh support until 2017. And as a result of Democrats pushing through the ACA, Republicans gained 63 seats in the House (a gain bigger than the 2016 "blue wave"). Democrats started out with large majorities of the Senate and House in 2008, and by 2014 Republicans had flipped the situation, with Democrats losing 13 Senate seats and 69 House seats.
In another example, if you asked people in 2008, most Obama voters would have said they wanted clean power. But they don't actually want to pay more at the pump or a higher electric bill. Hence Obama taking credit for fracking a major achievement of his administration: https://apnews.com/article/5dfbc1aa17701ae219239caad0bfefb2
3) Americans really hate taxes: https://news.gallup.com/poll/268295/support-government-inche.... Even in 2019, when 39% of people say they support "socialism" just 25% want a combination of "more [government] services" and "more taxes." (This is an all-time high! It didn't clear 20% from 1993 to 2013.) Meanwhile, 42% want "less services" with "less taxes."
4) People don't necessarily want the same things. Just because 55% of Americans want A and 58% want B, that doesn't mean there is a voting block comprising a majority that wants both A and B.
5) People who agree on a problem don't necessarily agree on a solution. The majority of Americans think income inequality is a problem: https://www.pewsocialtrends.org/2020/01/09/most-americans-sa.... But people don't necessarily agree on what causes income inequality and what the solution should be. Democrats want a big government to redistribute income. Republicans want to earn their money, and think that big government creates opportunities for the super-rich to earn income unfairly.
6) America is a Republic, not a Democracy. Elected representatives must balance (1)-(5) to give people what they want, not what they say they want. America makes way more sense if you realize that the government we have is what we can achieve with how much we're willing to pay (not that much) and how much we trust the government to do the right thing (not that much).