more things that finance is 'about' (eg the core compentencies of financial institutions, and the value that they provide to society):
- "money plumbing". Moving money from place to place (and more abstract versions of this, eg in between times); a more abstract version of the old traveling merchant.
- dealing with regulation: an oft-overlooked core competency of financial institutions is administering the necessary bureaucracy to comply with the large amount of government-imposed regulation around financial services
- "risk plumbing"/risk transfer: like moving money from place to place, except what is being moved is exposure to risk. This occurs because there are sometimes good investments with high risk (positive expected return but either low probability of success, high variance, large potential losses, etc), and so the person or entity best suited to find or manage the investment is often not the same person or entity with enough capital to be able to handle the risk
- cognition in Mr. Market's mind: price discovery. Information about reward magnitude and probability is combined into publicly available price information
- trust (brand): for example, you would deposit money in a savings account in a large bank with a well-known brand, but you wouldn't deposit the same amount of money in a supposed 'savings account' with a shifty-looking guy who hangs out on a street corner. Similarly you want trusted institutions to provide escrow services, etc. (this is the part that blockchain/cryptocurrencies might change; by using the technology of cryptography, some situations that formerly required a trusted third party can now be done 'trustlessly')
- capital cushion: financial institutions are often legally required to have a relatively large amount of money ("capital") sitting around with which to pay back counterparties in case something goes wrong. This might be seen as part of risk transfer, trust, and regulation rather than its own thing.
Out of these, the 'dealing with regulation' part is perhaps the most overlooked by people not involved in finance. It seems to me that a surprisingly large portion of financial company's costs are due to regulatory compliance, and similarly the answer to "Why doesn't <financial company> just do it this way, which is simpler?" is surprisingly often "Because that's not allowed" (or "because although that's technically allowed, it would require a more involved procedure to satisfy the law if we did it that way").