Concretely, how big is the throughput gap between Bitcoin and a system like Visa, and what trade-off does it illustrate?

Bitcoin sustains roughly 7 transactions/second (about 66 with security-preserving tweaks); Visa peaks above 50,000 — the gap is the price of decentralization.

* Log scale: even with security-preserving tweaks Bitcoin stays three-plus orders of magnitude below Visa's peak — the throughput tax of open consensus. *

These numbers make the abstract trade-off concrete: the more a system scales to many mutually-untrusting writers (decentralization), the fewer state updates it can process per unit time (throughput). Bitcoin's ~7 tps is the cost of open, trustless consensus; a centralized system like Visa skips consensus entirely and handles tens of thousands. When deciding whether to use a blockchain, this decentralization-vs-throughput tension has to be weighed alongside the "do you need it at all?" flowchart — a blockchain can be the right trust model and still be too slow for the workload.

Go deeper:

• Bitcoin scalability problem (Wikipedia) — where the ~3.3-7 tps ceiling comes from (block size, 10-minute blocks) and the tweaks that raise it.