This is such a grandiose topic that I can only throw out a couple of ideas. Some may not be particularly well thought out or well expressed but here goes. The main idea is to stimulate discussion.
Interestingly, the assets you mentioned (cash, HQLA) sound like the elements of liquidity measurement. Regardless of the source of financial stress, the ultimate event that usually kills a firm is lack of liquidity. Profitable firms have failed due to lack of liquidity. So there is an interesting and critical connection between capital and liquidity.
I have long held the view that some elements of the regulatory and accounting definitions of capital are of limited usefulness because: 1) they are backward looking rather than forward looking, and 2) the definitions fail to distinguish between the quantities of capital and the deployment of capital.
Where does one find the paid-in share capital and retained earnings of a firm? It is everywhere throughout the firm - some of it is held in cash and liquid assets, some of it is invested in core income-earning assets (e.g. loans), some of it is deployed in real assets (equipment, buildings, etc.), and some is even deployed in human capital. The point here is that some deployments of capital can practically be used to absorb losses but some cannot because they are essentially sunk costs with little realizable value (hence the connection between capital and liquidity). See where I am going with this?
As well, the capacity to raise additional capital (surely relevant) is something not generally reflected in regulatory and accounting definitions of capital. (Perhaps the view here is that a bird in the bush has no value?).
I am of the view that the first truly coherent book on bank capital has yet to be written, there is an enormous opportunity here. If I am wrong about this I'd love to hear about it.
So, just a few ideas tossed out. Hopefully the capital experts will join this discussion and straighten me out on all this.