That and the fact that the US is 1/7th as densely populated as the UK (UK is 260 people per km, the US is 34/km). The US is #179 on the population density list country wise. If someone won't sell you a piece of land, there's a vast supply of other land to look at. The only place you'll run into a problem is in a few high density metros like NYC.
Those are pretty dishonest stats though considering the vast majority of that land is extremely rural and much of it is owned by the Federal government (the Feds own 28% of all land in the country). The UK doesn't have something like Alaska which is both huge and empty (Alaska alone is 7 times the size of the UK, but has just 730k people).
If the US ever had a land crunch, it could easily open up vast new tracks of land for settlement via the US Govt. It's very valuable to have that ability. The Feds are already beginning to sell off their hoard of property due to fiscal problems.
I think there's definitely something to this, because land taxes aren't common in Australia, either, and yet almost all houses there are freehold house and land.
Doubtful. Land taxes are extremely common in Australia. All land is taxable, however exemptions exist for your own principle place of residence (ie home). If you own a holiday house or investment property then your are liable for land tax. That is the reason houses are primarily sold freehold as opposed to leasehold.