I.e. I don't get why the risky part of this loan can't be mitigated by the bank taking on the risk and managing it separately. Surely, there would be investors willing to back these types of collateralized loans?
Loans against other assets are much less risky, because they are backed by actual things. If the bank screws up in predicting the future value of a house, they can still own the actual house and land if you default. With stocks it would be far more risky because stocks are far more volatile than houses.
Because the risk of holding the stock is more than the difference in short vs long term capital gains.
If the stock is worth $1000 in gains, I know I can sell it and lock in the gains today and pay my normal income rate. If I have to hold it for another 6 months, there is a huge risk that it drops more than the 5-10% difference in the tax rate for the average person.
Other positions have a defined thesis and, if that thesis gets invalidated, I close out the position sometimes at a gain. I do try to make most of my gains be LTCG, but trying too hard to optimize capital gains rates can lead to poorer investment decision-making/asset allocation.
Now why don't you plug in this scenario into any Black–Scholes calculator and see how much of a net credit at entry you get (if you even have one). That would be the maximum loan amount you'd be able to get under this scheme. If you could get one at all, the loan amount is tiny compared to the value of the asset.
Banks don't take on risk. Seriously.
That's another conversation to have, but the simple answer is do you want the value of your checking account impacted by someone else's purchase of Gamestop, or Enron?
And that's why banks don't take risk.