Canadian (Or British) Sovereigns

At the time the Canadian Mint sovereigns were struck they were legal tender in Canada, but most if not all were sent to the UK.
Both Sovereigns and US Gold Eagles were legal tender in the early 20th century, they were mostly used for interbank transfers and international exchange.

They certainly were used as money, in Britain and throughout the Empire, though of course they did not "circulate" to the extent that the coppers or even the silvers circulated. A gold sovereign could buy you an awful lot in the early 1900s - it was roughly 1 week's average wage, so you wouldn't normally take one to do your grocery shopping. They weren't used as often in Canada, due to the awkward legal tender face value they were given (Can$4.8666666667, or three for $14.60). The Canadian-minted ones were mainly used in interbank and international transactions.

That being said, they were used for higher transactions, and gold is a soft metal so wears away much faster than baser metals. Gold coins can be found in worn, circulated condition. You just don't normally see them for sale in coin ships, because they're traded as scrap gold for bullion value. Why would you pay bullion value for a VG-grade coin, when you can pay the exact same price for an identical coin in EF?

In the bulk coin collection I'm currently sorting through, I've found a 1904 Perth half-sovereign in what I would call Fine condition. It appears genuine, but the high points are worn smooth, leaving St George more of a silhouette. The "P" mintmark is barely visible. It's lost 0.04 grams, or 1% of its mass. If I sold it to a dealer, they'd give me bullion price (currently about AU$200), and on-sell it for bullion price.

As with Canada, Australian Sovereigns were mainly used for international payments.
In both cases due to their use for international payments, they did not see circulation, although in the Australian case, Sovereigns did in fact, see very limited circulation. They were also used for payment between banks.
That is why they are now usually found in higher grades only.

Canada does not have a domestic Half Sovereign circulation history; Canadian Half Sovereigns were not minted. Do patterns exist?

I am not so familiar with Canadian sovereign history, (and so I stand to be corrected), but I suspect that they were also redeemable for Canadian Notes, such that they were a backup to the Note issue, under the Gold Standard.
Due to awkwardness of the Canadian Sovereign in exchange for Canadian Notes, the Five Dollars and Ten Dollars gold coins were minted instead.

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The Australian Half Sovereign however, was minted in only 10% of the mintage of the Sovereign, in accordance for domestic public demand for them for in circulation. Thus, the Half Sovereign is now normally found in much lower condition than the Sovereign, as well as being scarcer.
They circulated extensively in Australia alongside Ten shilling Notes up until 1914, at the start of WW1. Nevertheless, the Ten shilling Note in circulation was far more common than the Half Sovereign.
From 1914 onwards they were, for the most part, replaced with Ten shilling Notes from that date, but Notes could be still be redeemed with Half sovereigns up until 1933, when Australia came off the Gold Standard.

If you are drawn to things that are scarce, try to find a First or Second type Sydney Mint Half Sovereign, (1855 - 1870). They share a distinctive wreath design (non British), on the reverse, and saw extensive circulation as money. They are scarce, but not unobtainable. Up until 1866, they were alloyed with silver, not copper.

Fortunately for collectors this was not true and thus 100 years later we had the release of the Bank of Canada Hoard.