You might shrug and say "well pobody's nerfect", but the disparity between the American narrative and the reality is actually quite extreme.
Source: https://en.wikipedia.org/wiki/The_Economist_Democracy_Index
Look at the what The Economist is and promotes. I'd have about as much trust in Faux News Independent Press index.
I used to work and live in Poland for almost a decade (I visit friends there often), and I live and work on the UK and to be fair Poland seems far more democratic. Actual independence of the Judiciary, proportional representation Parliament, vacatio legis (as opposed to UK's "hey, that's your new tax code, effective immediately"), growing local democracies (despite 50 years of Soviet occupation, thanks to the betrayal from the West).
I don't think anybody who has actually lived under a pre-democratic regime would call the US "no way democratic". There are many democratic aspects of the US, and it has reasonably strong institutions. But it seems that most Americans have not yet realized what category they're in, and think that the US is some kind of front-runner.
Source: https://en.wikipedia.org/wiki/The_Economist_Democracy_Index
A multitude of different peoples voting to rule over the others is not democratic and will never be democratic. Just because the voting process is secure does not make it democratic. What makes it democratic is that a people rules themselves, nothing else.
Zulus ruling over Xhosas is not democratic just because the Zulus give the Xhosas votes because Zulus and Xhosas are two different peoples, and contrary to popular belief, soil is not magical and a Xhosa born on territory ruled by Zulus does not make him a Zulu.
Jews ruling over Palestinians is not democratic just because the Palestinians have votes because Jews and Palestinians are two different peoples, and contrary to popular belief, soil is not magical and a Palestinian born on territory ruled by Jews does not make him a Jew.
Reinventing the dictionary will only confuse you, it won't change reality. Nominalism is not only stupid, it's wrong.
Democracy is not just voting. Actual full democracy is predicated on a fairly large number of fundamental rights, as well as duties. Democracy is antithetical to majority rule, in which the rights of minorities can be ignored or trampled by the majority.
Zulus ruling over Xhosas can never be democratic, because nobody is "ruling over" anybody else in a democracy, no matter their ethnicity, religion, gender, sexuality, and so on.
Some people call what I'm describing here "liberal" democracy, but that's to distract from the fundamental fact that there is no meaningful definition of democracy that isn't liberal. If we're not free and equal, we cannot participate in democracy, and therefore it isn't democracy.
On the other hand I don't know a solve for every bill having less than a handful of votes that are bipartisan...
After all the federal budget is so large because you can swap states but you can't get away from the IRS.