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.
I wouldn't have the balls, but got a friend who took on a huge loan (about 3x his annual income) and bought BTC @60k.
he is able pay back the full loan + interest with his income over the years while his BTC stash gains value against the fiat he borrowed.
If he looses his job... too bad, his BTC are already on some addresses nobody has access to apart from him.
I really consider it a smart move without too much risk...
I shamefully took out a loan against my Bitcoin using Coinbase. I wanted to test it out and see how it worked. I decided to buy Solana with it to try out a carry trade since the rates were cooperating. This was a few months ago when SOL was scraping bottom. I’m currently up about $20,000 and have begun paying off the loan. I’ll probably leave the profits staked forever similarly to what I did with ETH after the Hex airdrop… Free passive income forever is cool. As to not completely leave Bitcoin behind from this trade (you can breathe now), I did put some of the profits into a wBTC/SPYx liquidity pool, so I’m also earning passive wrapped Bitcoin as well. All without ever selling a single satoshi.