The problem with your approach is that you're relying on the government to decide what items are necessities. In the UK, politicians seem to think that it's not necessary to wash, because most personal hygiene products are subject to the full 20% VAT rate (although they concede that it's more difficult to avoid menstruation, as 'feminine hygiene' products are subject to the reduced 5% rate). You can't buy these items second-hand. Likewise for other domestic cleaning products, and almost any consumable that isn't for human consumption.
Do you regard electricity as one of life's necessities? How about gas or oil for heating? 5% VAT. The government thinks that heating your home during the winter is somewhat optional. You can't buy energy second-hand.
Second-hand purchases are a solution, but only if you buy from people you know. eBay? That's a long way for a shortcut, seeing as you need a computer and an internet connection (both subject to 20% VAT). Second hand store? They're have to charge VAT on the items they sell. And if you buy from a man on a street corner, you're not going to receive any kind of warranty, so you could end up out-of-pocket further down the line.
One of the mantras you hear regularly from libertarian types on Slashdot is, "I know how to spend my own money better than the government does". I think the same applies here. Poor people know what the necessities are, far better than the government does. If you scrap VAT, raise the personal allowance to £10,000 (as the Lib Dems recently proposed) and raise the standard and higher rates of income tax, you can ensure that the poorest people have what they need to live a normal life, while still giving an incentive to earn more.
Many genuinely rich people don't pay any income tax at all, as they have no income (on paper).
I'm fine with not taxing people who are living off a big pot of savings. Income tax should already have been paid on that money.
If you're referring to the various ways that rich people with expensive accountants can avoid paying tax, then yes I acknowledge that problem. I would rather that the government invested time and effort into closing those loopholes (which they have an incentive to do), rather than attempting to overhaul the tax system in the way that you are proposing, where the government is incentivised to fiddle with the 'necessities' list in a way that impacts the poorest.
It sounds to me like you want a truly fair taxation system, without inequalities. If you want to do that sort of system, there is another that would be better than an income tax and would be very simple. Take the total government budget for the year and divide by number of people in the country. Children's taxes must be paid by the parents. It's only $11,370 per person. Seems very affordable to me.
Now you're just being obtuse. What you describe is a regressive tax, and is the most unfair method of taxation in existence because it isn't linked with a person's ability to pay.
You're not the only person who has described such a system as 'fair' before. Margaret Thatcher did. It was called the Community Charge, but more commonly known as the Poll Tax.
When it was introduced in Scotland (a year earlier than in the rest of the UK), it led to mass non-payment and civil disobedience. It's one of the reasons that the Conservatives are now almost unelectable in Scotland, and 'Thatcher' is a dirty word here. The fact that the Scottish wing of the party (what is left of it) is debating whether or not to split from the UK party and undergo a massive rebranding exercise is in part a legacy of the Poll Tax.
And finally...
Heck, I'm not poor, but I have over $100k in student loans to pay off with my meager earnings after the government takes over 50%
To use your argument against you, a university education is an optional purchase.