Why would you want to get a loan in paper bitcoin, though?
I don't

But I can imagine bankers coming up with this scenario
for profit.
Why not take a loan in paper dollars, and use them to buy bitcoin? This way, you don't have counterparty risk (bank going bankrupt, or practicing fractional reserve with no reserves), while you do borrow the bitcoin. You're also increasing the supply of dollars, while decreasing the market supply of bitcoin, driving the price up.
I wouldn't invest borrowed money, but I'm risk-averse when it comes to loans.