While I'm personally for single-payer healthcare, I don't see why going off on your own means you should get to pay less in taxes than someone who has to work under a boss. Does it incentivize economic growth? You're not hiring anyone...
Self-employment comes with personal financial risk, but the reason for their lower national insurance contributions (NIC) is to do with pensions. The UK chancellor this year:
> Historically, the differences in NICs between those in employment and the self-employed reflected differences in state pensions and contributory welfare benefits.
Self-employed people are more unlikely to have a pension, and the state pension is about £7,000 per year.
In contrast to this, people who are employed have access to a workplace pension, where an employer must contribute to the employee's pension. The average teacher will have a workplace pension of £25,000 per year.
So, the idea behind the reduced NIC for self-employed people is that they'll put the money into their savings / personal pension. If you're self-employed and adding 3% of your income into your pension each year, then the 3% savings on NIC would be the government enabling you (as your own employer) to 'match' your own annual pension contribution.