The Jones Act also bans registering a vessel in the US if it wasn't built there. US shipbuilders are happy serving the captive market, so if you want one to build an LNG carrier it'll cost at least four times what Samsung charges.
If the US had an open registry, there would be US-built LNG ships; there's no shortage of competitive American shipbuilders that make vessels small enough to be exempt. But the Jones Act pissed that away, as protectionist laws invariably do.