I wouldn't say they cannot be kept in captivity. See, if you have the money, time, and land you could have an enormous aviary built over a large, established lake with a steady population of breeding fish, (you could also introduce large batches of young native fish every year to boost the populations) then it could theoretically be done.
Also you'd need a whole load of permits in the US, although in Canada you'd need an aviculture permit for migratory birds, which would allow you to collect the eggs of loons, and hatch and raise them yourself. You could hatch the chicks under a broody hen, and keep them in a wet brooder type setup until they're fully feathered by which time you could release them into the aviary. When they're young feed them fish sized proportionally to their body, and somehow teach them to dive and catch food. This is a highly ambitious, unfeasable idea though.