Without a fractional reserve system, the liquidity that drives all economic activity grinds to a halt as everyone fights over the few remaining real dollars rather than managing their deployed capital.
Banks basically act to multiply the amount of money in the world today by creating promises about the future that act as a bridge that moves money from the future into the present. That money then flows into restaurants, dog walkers, software engineers, etc... Inflation is kept in check b/c the promises force the money to be paid back to the bank via monthly loan repayments.
Banks that only hold short term reserves or cash equivalents like Brex don't act as this multiplier. Going forward it's likely small banks will move towards this model as only the big banks that are too big to fail (b/c they are necessary as multipliers) can afford to take on the risk of longer term investments or creating loans.
But that doesn't really provide that much interest to depositors, in this age of loose money supply.
So there are more exotic functions that "investment" banks fiddle with. Ie trading on the stock market (regulated betting) buying companies, and trading on futures and other pure bets.
The problem is that banks are bigger, and have more depositors. So when one pops, other go because they are all doing the same shady shit to make profit.
In the UK there are still a few building societies that offer traditional, boring, consumer banking and mortgages. But they are now large national behemoths.
But to your point, Brex is a payment manager/facilitator. Its not really offering banking, its more a service to manage expenditure. This might seem like pedantry, but its different enough to make the point.
To your point about risky investments, like stocks, I agree that that's very sketchy. But I think even very prudent banks that don't invest in stocks etc still take on a lot of risk, like we see with the bank collapses caused by the high interest rates these days.