One of the primary purposes of government is to redistribute wealth, by reducing the rate at which it accumulates in those parts of the economy where it tends to do that; And by injecting money into parts of the economy that tend to become impoverished.
Taxes are money taken from selected parts of the economy and destroyed They do NOT pay for anything. Government spending does not rely upon taxation in any way. Quite the reverse - taxation follows spending, it doesn't precede it. Government finances are nothing like household budgets, where you can't buy stuff until you get your paycheck; Government finances are the exact opposite - If you are a currency issuer, you can't collect taxes until you have created an economy, by spending money.
As an individual who believes that many wealthy people (including himself) do not pay sufficient tax, Warren Buffet is completely correct to lobby for a tax increase for all citizens in his position, rather than to simply choose to pay more himself - And to suggest otherwise simply indicates a fundamental lack of understanding of what taxes ARE.
Taxes are not theft, nor do they pay for stuff. Taxes are a way to ensure that money doesn't all end up concentrated in a small number of places, where it cannot do useful work. To be effective, the tax structure needs to be universally applicable - everyone who qualifies to pay $X should pay $X, no matter how much they think or feel they should pay.
If an individual believes that a specific person, organization or program should be better funded, then they should by all means give some money to that person, organization or program. They can also (or instead) lobby for government to increase funding to that thing; Or to begin funding that thing. But government funding has FUCK ALL to do with taxes, so paying extra tax would be completely ineffective, and nobody sane would contemplate it. In fact, the idea that it might be a good idea to pay extra tax if you are in favour of higher government spending is a powerful indication that the originator of the idea hasn't got a fucking clue how any of this works.
It's as smart an idea as setting up floodlights to illuminate your solar panels, so that you can have electricity at night.