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 debt.
Here is how I do debt. EVERY 14 months or so I take out a new Credit card.
It has to have
1 a bonus for 1000 or more purchase
2 cash back on purchases
3 15 or more months to pay it off with zero interest charges.
One more thing if I buy say 2 antminer s21xps at a cost of 13,000 with 500 back in bonus. I owe 12,500 with 14-15 months to pay it. The key is I have to have 12,500 cash on hand to pay it off and about 4,000. Cash on hand for power bills.
Let's analyze this.
0 money up front.
500 back in bonus
And the gear earns 540x0.00000051=0.0002754 btc a day.
So I generate 0.0082 btc a month