This is a very simplistic argument that neglects one of the key problems. Geography. Not all votes are equal. In the UK and in the USA, it isn't a matter of who votes - it's a matter of where those voters are and how important that area is to the overall strategy of the politicians in question. Most people don't bother to vote because there's very little point doing so in safe seats. Or.... like my parents, their votes sometimes cancel each other out - so they don't bother.
We aren't democracy, we are the demos. The way the boundary lines are drawn, the process and the system is Democracy.... and it's broken. That's not the fault of the left or the right, it's the fault of both - both have sought to undermine the democratic process with modern technology. The right have diseminated information they know to be factually incorrect via social media, the left have attempted to use social media to control discourse and language through cancel culture. Your 'tyranny minority' applies equally to both sides of the political spectrum but in different ways.