I did a quick'n'dirty test the other day, just using the sweep hand of my watch for timing.
After 30s the water from the hot tap in the kitchen was 40°, so it would have taken < 30s for it to be OK for handwashing or to start filling the sink. After 60s it was at about 55°, which is uncomfortably hot for handwashing.
With only a measuring jug to hand to measure flow rate, I timed 1l in 6-7 seconds, so 30s would have seen 4-5l flow, and 60s 9-10. Technically gallons, not sure if "several" would be correct.
Boiler is in the kitchen, probably 3-4m of pipework to the taps. I suspect distance is the main factor, and as you say, things are unlikely to be significantly better with stored hot water, particularly if it is used to heat water, rather than directly.