If the large and politically connected banks and brokerages have losses large enough to threaten their survival as institutions then the government will jump in to help secure them and bail them out if needed.
I would stick with a "too big to fail" institution instead of splitting across multiple.
If you want a real "backup" you could ask for physical stock certificates or get physical gold or something else that cannot be taken from you by computer hacking.
How is the government going to help secure them? Do they even have enough qualified people?
Well I assume there are some smart hacker / security people in the NSA etc. who could be parachuted in to help if it really came to that.
I think these banks will probably be able to hire equivalent people in the private sector though and might not need the government help.
I work in infosec and work with many of these large organizations.
Simply put I don't think dropping in smart people in dysfunctional organization is going to have instant results. It will take a pretty long period of time to make them aware of all the systems with holes.
In the meantime hackers would be running off with actual information and money. More than likely I see banks turning off all kinds of systems in a panic and people with their money there being in an even bigger panic.
FDIC insures deposits up to 250k. Big institutions basically all have this government backing. If an incident occurs, FDIC has deposits available next business day in event of a bank failure
FDIC insurance is mostly unrelated to this. If someone hacks a brokerage, sells a bunch of customer assets for cash, adds new bank accounts for those customers, and then withdraws that cash to those new bank accounts, FDIC insurance does not help at all.
Another bad one I've heard, buying thinly traded penny stocks as a way to exfiltrate money from brokerage accounts without wiring.