The state monitors financial transactions primarily for tax purposes. I'm guessing a very substantial amount of data they collect is around payroll and sales.
The state monitors transactions first for illegal activity under mechanisms like the Bank Secrecy Act (BSA). Any payments or financial services company follow Know Your Customer standards including running OFAC checks to ensure that the recipient is not a known terrorist.
"Monitors" is a bit strong, unless you're talking about actual states. NY/NYC will go after you fiercely if you are wealthy and try to get out of city taxes.
All federal tax information for employees is self-reported by employers. There isn't a huge monitoring infrastructure in place—just required-by-law reporting of what people get paid. Getting paid with not-dollars doesn't change the system.
To be fair, there's also a strong contingent within the U.S. political right that believes paying taxes should be made as explicit (and, potentially, annoying) as possible, lest the citizenry fail to appreciate how much of their income is being extracted to fund the government. This kind of thinking has popped up on the left from time to time as well, around things like military spending.
The solution there is just to get a receipt showing the breakdown. W-2's are kinda that already at a very coarse-grained scale.
We don't have any system in place to show military spending breakdowns or get people upset about it or give people who are upset about it a way to influence changes shrinking it in the future.
