However, pairing that with a proof-of-work consensus mechanism is incredibly inefficient, energy-consuming (requires at least 50% of all available compute to be engaged with the blockchain or risk bad actors taking over).
As-is, the cryptocurrencies we've seen have all been incredibly wasteful and inefficient. Any that would be efficient, both energy-wise and for speed-of-transactions would most probably require ditching complete decentralisation and thus be unacceptable to hard-core ideologues in the "crypto space".
For a rough estimate of the "transactions per second" you'd need to be a global, practical, "we handle all transactions", we can do a rough estimate. There are, what, 6 * 10^9 people on the planet. At a conservative guess, each person does about one exconomic transaction per day. Let's assume that is approximately evenly distributed through each day. A day is 86400 seconds, that's close enough to 10^5 that we might as well use that. That gives us at a minimum 6k transactions per second to be viable for a single global electronic currency.