My personal argument for listing them in the general section is based on two primary things. First, if we decide to list them in provinces, all cast coinage from the Qing dynasty would need to be placed there, since they are separated based on the manchu on the reverse, alongside many older coins. For the older dynasties, it would also make it so the catalog would be weird. As an example, let's take Emperor Ningzong:
- N#141271 would be placed in the general section since it was made at several different mints in different provinces.
- N#219347 would be placed in Anhui, since it was specifically made at a mint there.
- N#221093 would maybe need a separate section, since it has a character on the reverse that is (likely but not with 100% certainty) referring to a mint, but it is not which one.
This would therefore make the catalogue pretty weird and inconsistent, and you would have to search in different sections to get similar coins.
Another point on this is that the provinces vary between different times. If we take N#219347again, the place of minting would be in modern-day Anhui, but according to the provinces of that time (according to this map on Wikipedia) would be Huainan West. So that would mean that we would need to add probably 100+ different provinces based on both the division in different dynasties and how they change.
As a second point, I think they should be listed not where they were made, but the issuer of the coins, similar to counterstamped coins are listed in the country they are counterstamped in, and not the country the host was made in. If we take the original coin in question, it has the emperor's name on the obverse and what effectively is a mintmark on the reverse. This just meant it was made there, and not that it was issued there. You can compare this to modern-day coins with different mintmarks. Let's take N#44 as an example. The different mintmarks on that coin (D, P and S) have the same function as the Manchu in these cash coins, but are still listed in the United States and not in Colorado, Pennsylvania or California, since they were made, but not issued there.
Compare all this to N#62144 as an example. On that coin it specifically states “KIRIN PROVINCE”, referring both to where it was made, and as a specific issuer.
And regarding your argument for putting them in provinces, your first point is not valid since on the pages in numista the places of the mints are stated (however, they don't refer to the different provinces at the time, so you could argue that should be added). And regarding your second point, you could just put the name of the province in the search bar and (assuming the correct mint is listed) you would get those coins. Besides, I doubt most people, use a KM catalogue to identify these coins, and use Hartill instead.