Let's be honest here, what we're really talking about is shifting the burden of taxation more onto higher earners. It sounds very nice to give lower earners more money, but it brings into question the definition of 'fair'. The obvious point to make is that higher earners already pay more tax both on a gross and a proportionate basis. National insurance is paid for pensions and various benefits which are available equally to non. low and high earners.
You have a table of taxation input according to earnings, but for the sake of fairness, you need to consider outputs too - child benefit, income support, pension credits, tax credits, jobseekers allowance, housing benefit. If children go to a private school, there is less burden on the public education system. Private healthcare means NHS resources are not spent on those who opt out.
You also need to consider that removing NI will make it easier for high earners to mitigate their tax bill by employing partners and children. Currently, with the NI cap, employing a partner on a salary of £20k entails additional NI contributions which reduce the level of net pay to make any savings marginal at best. Removing NI will encourage this form of tax avoidance which benefits exclusively higher rate tax payers.
Lastly, anyone suggesting that employers wouldn't trouser the 13.8% saving on their NI contributions has more faith in their altruism than me.
Perhaps the current system isn't fair. The scrapping of the 50% income tax rate should be reversed, for example, but a basic analysis of income based tax inputs is just scratching the surface.