Depends on your view of the role of the government. It only matters if you think that 100% of earnings belong to them...and not the citizens.

It doesn't matter in the context of what we're discussing. Government can subsidize things using different levers. They can just pay money directly to subsidize it, or they can relinquish a tax obligation in the same amount. Because money is fungible, it doesn't matter which they do - the impact on the product's market is the same.

Nope. Relieving someone of a tax liability on income means they have more cash to spend on a variety of thing, whatever they want. Targeted subsidies only affect the thing being targeted. They're not the same, not at all.

I thought it was clear from context that the 'sending them money' option would be under the same conditions as the 'relief from tax obligation.' For example, if you send someone $100 for doing a specific thing, it has the same effect as relieving them from a tax obligation on that specific thing (ie. sending them a check in the amount of sales tax on a car or waiving the sales tax on the car). Alternatively, there is also no difference between sending someone $100 with no strings attached and relieving them of a general tax obligation of $100 with no strings attached.

Again, money is fungible. So there is no economic difference between a subsidy that takes the form of relieving a tax obligation or one that involves a direct payment. If I decide to send all waitstaff a check in the amount of 9.2% of their tipped wages, or if I grant all service staff an exemption from their income taxes for their tipped wages in that same amount, it has the exact same effect on the waitstaff. And on all other taxpayers - I have to come up with that money somehow, and (since money is fungible) there's no difference to the Treasury whether the deficiency is styled as a $X expenditure or a $X reduction in revenue. Either way, I have to make up that money from somewhere - either taking money from other taxpayers or cutting services given to other taxpayers.