Is there evidence that this is the right way? Because it seems to be far less efficient than other ways if funding charitable causes directly by a significant margin.
Painting with a very broad brush, the US is the most charitable country in the world, yet we lag behind many other countries according to various measures of human welfare.
The US was the most charitable nation in the world but it's not a given.
I think this depends quite a bit on what you're trying to achieve. Hard to measure effectiveness otherwise.
E.g. if you care about global human welfare (and setting aside longtermist ideas), the most effective use of a marginal dollar is to donate money to people in poorer countries (via various methods). One of the main reasons is that the richer countries have a much more robust social welfare system already via taxation.
I'm sure there are good nonprofits/charities. And there's definitely inefficient public offices that are mainly interested in politics.
My point is "seems less efficient" is kind of weak ground to be asking others for evidence
You don't have to have a 'sense', you can look up the overhead for some nonprofits to look and see how much is spent on compensation vs giving/redirecting money to their causes vs. ancillary expenses.
It's often much less than the government in terms of overall efficiency.
Charity incurs oversight burdens. The UK has a long story about failures in charity, the charity commissioner has had to intercede many times. It would be wrong to assume there are no oversight costs, the thing is that to the charity they may look like externalities. They have to be borne, the state bears the cost.
Charities also usually cannot intercede politically to fix the situation demanding their charitable work. So, charities are excluded from lobbying in some ways, where governments reflect the will of the people and are subject to both good and band consequences.
Charities are abused. Churches for instance. Why do churches qualify for charitable status, when they (in most economies where they are or have been) are established entities with massive landholdings and wealth?
In the end, it's a matter of philosophy. Without being patronising, I tend to think right wing people who believe in personal responsibility and low taxes favour charity because it gives them discretion, to give or not, as a function of how they feel about the recipient, and left wing people who believe in the state as a construct reflecting popular will believe in state functions to implement the burdens individuals cannot manage for themselves.
I say that because my very good friends who donate highly tend to be right wing and tend to make moralising statements about diabetes being a function of a lack of personal self control and so do not fund interventions to prevent diabetes in the working poor because "they lack self control" and also chose not to fund womens reproductive rights on similar grounds "chastity is its own reward" -Bill and Melinda Gates were exceptional in ignoring the fundamentalist christian lobby which came into the room in the Reagan "just say no" years, and funded contraception and abortion in Africa regardless.
That would take much of the corruption out of it. These donor advised funds now allow someone to maintain full control of their money while the IRS considers it 'donated' it for a major tax write-offs.