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So, again, a tax on income is not a tax on the source of that income.

A useful point about the immediate source of payment of the compensation paid not being taxed where taxation in regard income received is concerned, the cites will be useful in other contexts. That however and has little to do with the fundamentals that I was expressing.

For your statement misses the prime issue, that the subject of an indirect tax is the activity or exchange engaged in and not the compensation used as factor in measuring the amount of the tax to be paid.

That activity or exchange is the essential, that "property incidental to ownership" that classifies a tax as indirect as opposed to direct (where tax is levied merely because of ones ownership.)

To not tax activities or exchanges the same for government as for the individual causes economic dislocations and is the essential reason it makes sense to tax government purchases of goods and services the same as you would household purchases of goods and services.

The case of purchasing services without a tax paid by government agencies, which government could legally arrange and you apparently advocate, creates a situation of net advantage to government agencies in purchasing resources away from the household's access to them at cost lower to government agencies than is available to the household which is taxed.

Essentially the government is able to offer a compensation higher, by the rate of the tax, to the service or goods provider outbidding the household in competition for the same pool of resources.

Not taxing government agencies operates to deplete resources from the markets reducing the supply available to the private sector. The same principle operates for goods as well as services drawing resources away from consumer applicaton and into government utilization.