Supplying a single 1 GW(e) burner reactor with seawater uranium would require a 170 square kilometer absorber field on the continental shelf. That's much worse power/area than solar, and just slightly higher than the power/area of an offshore wind field.

Of course use of breeder reactors could extend this, but with breeders terrestrial U resources are adequate for a very long time.

Sir. There's a practically unlimited quantity of uranium available to meet our energy needs now and for as long as humans wander this rock. To claim otherwise is disingenuous at best. A huge reason breeder reactors aren't used right now is that there's plenty of land-based uranium already and fuel is not a concern. So much so that stretching it with breeders doesn't really matter, and as a percentage of the cost of generated electricity the uranium input barely registers. By the time we need to dip into the renewable water-based sources, we'll long since have been carbon-free. It'll scale just fine. Stop worrying about problems that won't matter for 10-100,000 years. We've gotta clear the century first.

There is a pratically unlimited quantity if cost is no object. But for cost to be no object, breeder reactors are needed. For burner reactors, fuel cost will begin to be seriously affected rather quickly if we try to supply a 100% nuclear world economy with only terrestrial U sources. That economy would go through in excess of 1 million tonnes of natural uranium per year to supply the current world average primary energy demand of 18 TW (about 6000 3 MW(th) reactors.) This could exhaust known terrestrial uranium resources (not proven reserves) in less than a decade.

Breeders, as I said, would greatly extend the terrestrial U resource, both by getting 100x as much energy per unit of natural uranium, and by allowing resources 100x as dilute to be economically exploited.