On the $100 bill
Edit: Parts of this post are meaningfully incorrect. Specifically, the Fed prints on the order of 100s of billions (not 100s of millions). Will be updated soon.
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This is Ashok. 
I would wager that 90% of all tax evasion has nothing to do with cash at all; tax evasion via cash transactions at the small business/consumer level is infinitesimal compared to that practiced by people and corporations with highly-paid tax attorneys; their money never actually materializes out of the electronic records of the banks.
Steadily eliminating cash accomplishes two things for the plutocrat’s technocrats such as Summers, hidden behind their ‘anti-crime’ facade: it enables much deeper tracking of who buys what and when (and who has ‘too much’ money), and it enables their cronies in the banking industry to skim ever more off the top.
An example: my brother (who works for a major fast food chain whose name seems vaguely scottish) is paid his pittance via direct deposit; his bank skims a transaction fee then, and transaction fees when he wishes to withdraw money, even as an electronic trade, which costs as close to nothing to accomplish as you could get, since he’s not wealthy enough to maintain the minimum balance needed to avoid said fees.
Multiply this by the millions of people in this situation and it’s clear that it’s a big profit center for the banks. They make loansharks look like kindly neighborhood philanthropists by comparison.
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typo loosing -> losing. (feel free to delete this comment after fixing)
For reference, US$100 is not the highest value banknote. EUR500 notes circulate and, I think, are the highest value in circulation. There are some GBP 100mm notes, but they don’t circulate. Fun BOE coffee break prank: trying to pay for your flat white with a 100,000,000 pound note.
GBP 100 is also higher value than US$100; there might be others in other currencies.
When the EUR notes were introduced, one popular story was that they were intentionally targeted toward illicit users, so the ECB system could capture more seigniorage. Maybe they were just anticipating the eurozone crisis and cross-border capital flight.
The “$100 premium” is actually a small notes fee.
The $100 notes fetch usually the central bank rates (where currency is free), but exchange offices hate small notes. So they charge x% fee on smaller notes, which increase for the smaller denominations
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