Every time I think I understand how modern money works, I learn about something like this.
Ultra-large denomination bills are a relic. They preceded computerized records as an immutable record of interbank transfers.
For example, say someone in New York sends someone in San Francisco $100 million. Settlement-wise, the New York bank reduces the sender's deposit balance and moves reserves from its New York Fed reserve account to the New York Fed itself. The New York Fed moves these reserves into the San Francisco Fed’s account at the New York Fed. (These could, at the San Francisco Fed's option, then be couriered across the country.) The San Francisco bank, in turn, gets $100 million deposited into its reserve account at the San Francisco Fed and creates a deposit in the recipient's account.
Keeping track of all of the above is complicated. Physical settlement, in a country without the telegraph, reduced the risk of errors. Moving around tonnes of cash is inconvenient. Hence, super-large bills, used solely for the settlement layers above.
Considering inflation a $100 note today is comparable to a $10 note from just a few decades ago. Thus currency denomination should shift in the opposite direction eliminating the cent and nickel, and adding larger notes.
Bypassing Congress seems to be the main thrust of the plan since, if Congress wanted to, they could pass whatever laws they like. This is, Congress could get a similar effect without actually printing a coin if they wanted to.
The issue seems to involve some complicated interactions. For example, Congress likely doesn't want such printing as it may weaken America's reputation for economic integrity. Also, it seems that a lot of modern politics centers around Congress having regular battles over the budget, such that breaking that paradigm would seem to shift American politics away from the current status-quo.