Pause on the issue with 'having security for a loan' for a moment [it seems to be clouding the economic reality of what you are presenting]. Your plan is for a bank to lend your hypothetical broker money. The bank then charges the broker an interest rate. And then the broker... pays for that with a higher interest rate they earn by buying T-Bills?
So why wouldn't the bank just buy the T-Bills?
The point is that the t-bill rate offered by the US government is basically the lowest possible interest rate there is - on the basis of the US government being considered the lowest USD credit risk for possible default.
In order for the t-bill rate to be higher than your broker's charged rate on its loan from the bank, the bank would need to consider your broker to be a lower risk of default than the US government. This doesn't make any sense - it is self-evident that any random brokerage house has a higher risk of bankruptcy than the US government. Your broker has no army, has no ability to raise taxes, has a workforce of maybe a few dozen [or perhaps a few thousand] instead of hundreds of millions, has no recognized rule of law... well, you get the picture.
You say that this debt to the bank is 'very secured' because of the stock assets held by the broker [forget about the fact that the broker does not own those assets, and therefore has no ability to securitize them] - yet surely you can see that the security offered by the US government is greater. Therefore, t-bills should have a lower rate of interest than this private debt, and your plan simply has no value.