> If the vast majority of the public actually agreed on something

Huge ask right at the beginning. If that is met, there are several examples such as The Velvet Revolution, Iceland's Financial Crisis Protest, The Women’s Suffrage Movement, Philippine People Power Revolution (1986) etc.

Such a huge ask, I think that most of western society is not in a state to be able to fulfil it. Especially in the US and UK (but probably many others), we've become so polarised that there's some kind of perceived honour in opposing the other 'side', regardless of your own actual opinion. If we needed to fight for suffrage today, for example, I don't think there would be a "vast majority", just two roughly equal sides taking opposing views for the sake of it.

Well, the internet has finally helped realize the politician's dream - making the voter believe that:

    1. They are in the right (no pun intended) group
    2. All other groups are in the wrong
    3. Their leader cares about them 
    4. He/she has the solution

When the reality is:

    1. Most of us are in the same group
    2. The group is of screwed over people
    3. The leaders only care about gaining and staying in power
    4. Why would the leaders find any solution that won't help with gaining and staying in power?