Mercado:
I see two main reasons why the .223 is not so popular, but there may be many more ...
1. The caste bullets will be too long for feeding into most magazines...
2. Airgun manufacturers are not interested in "Custom Builds", their business is mass production of guns that will use commercially available pellets
Regarding the Ballistic Coefficient: You mention that a .223 cast would have better BC than a .22 and this is partially true...It will have better BC because it will be longer compared to commercially available slugs/pellets, nevertheless, if you elongate and add mass (weight) to a .22 slug or a pellet to a point where it is as long and as heavy as the cast, the .22 will outperform the .223 or .224 but both bullets will have the inconvenience mentioned in point 1 above..
For shooting 45 gr. in a .223-.224 at 990 ft./sec. you will need a huge regulator pressure, even using one of the new Impacts with Power Plenums, the higher the pressure the more wear of parts, the less shots (less efficient gun) and the less precision...From what I've learned, most of the people participating in this forum put efficiency and precision over energy.
Some 10 years ago I tested some of the best .22 Rimfire barrels that were used in .22 Rimfire BR competitions...Those were all .223's MI Barrels (Note: MI means minimally invasive) and I opted for slow twists (1: 24 and 1:28 TR's) and 3 & 5 land/groove combinations...I didn't obtain any big energy advantage over a lighter .22 pellet shot at a much higher velocity so the energy levels would be comparable...We then tested a .172 barrel with commercially available 20 gr. Sierra bullets that have a .125 BC, the project was very attractive but the cooper jacket generated much friction that turned into low velocities and we immediately aborted any further research, it may work with a custom slightly over sized barrel but we lost interest in pursuing this project. Other than experimenting and learning I don't see any justifiable reason for setting up an airgun with a powder burning barrels/bullets given the commercially available slugs and excellent pellets.
If we are realistic with the capabilities of the gun we are using, a .22 slug will give us enough energy for varmint shooting up to a coyote size animal maybe up to around 80-100 yards or maybe a little further if we do our part..A .30 will be better and if you get into the .45's and .50's you will find people shooting Cape Buffaloes with those calibers...We've shot some wild boar in TX with a .30, but boars are extremely tough and hard to kill (body shots) but no so much if you shoot them in the head...
There are many slug molds out there with commercial airgun pellet diameters (.177, .22, .30, .35, .45 and .50), I've seen cast molds that are OK but the best are of course are the swagged slugs. With swagging molds you can make them hollow point with flat base, dish base and even hollow base like a pellet (FX Hybrids) and you can also have a full hollow body that will allow with any of the bases mentioned that will allow lower weights with high BC's...Not cheap but if you are an enthusiast and have the resources this is in my opinion the way to go.
Best regards,
AZ