It sounds like you're talking more about things that could help middle class people. Very few poor people have issues that could be helped with "pay [themselves] a minimum wage and make up the rest as a dividend".
The reality is different for poor people, but my point was more about "what could be", rather than "what is". Trying to think about it in terms of the current system is flawed, because the current system is designed to enrich people.
If everyone was avoiding tax then the tax would need to rise, or the laws would need to change - this may or may not be a good thing to the masses - but it's certainly not a good thing to the rich - which is why they make sure it doesn't happen.