The purpose of a system...

is what that system does.

What the system is actually observed to do; it doesn't matter what people say they want it to do, or it is meant to do, or is trying to do; the purpose of the system is what the system is actually observed to do.

If you want different behaviour, you need a different system.

One of the major problems with "too large to fail" financial institutions is that the system we've actually got is one in which the people running the institution make millions of dollars irrespective of the performance of the institution. (Canadian chartered banks aren't particularly bad about this, but they're not good. Everywhere else is apparently worse, which horrifies me.)

There's absolutely no need for a dedicated financier caste; there may have been, way back when finance was about personal reputation and letters of credit and moving gold around a hostile landscape, but in a world were money is increasingly not merely an abstraction but an electronically mediated intangible abstraction, and there's any number of numerate, educated people who would be quite happy to do the job for a modest professional salary, there's absolutely no need to treat people who work in finance as special. (No one's special, at the level of public policy.)

It's very easy to define a bank as any institution that takes money from a member of the public and either stores it or invests it on that individual's behalf, and which is, as a bank, constrained to compensate its employees, officers, directors, and members of the board no more than some small integer multiple of the median family income for that country. (I would suggest that this integer multiple be selected as 3.) This is total compensation; salary, stocks (priced at larger of the market price at time of grant or exercise), mobile phone plans, provided car, everything.

If a corporation is a person, it's a member of the public.

If a corporation is not a person (and I don't agree that they are), I still can't think of a reason for the rules to be different for taking a corporation's money and a natural person's.

No single bank can have more than 3% of the market. If a bank exceeds that size, it is immediately liquidated. Not sold, split, or otherwise altered and continuing, but fed into the existing provisions for the winding up of a business under the bankruptcy laws.

I can't see how this would do any harm to the provision of financial services whatsoever, and it would provide the considerable good of removing working in financial services as a plausible means of accumulating great personal wealth.