Because it's not their (core) competency or they don't want the risk.
I could start my own company printing indie games. But I have no connections in the industry (well, not entirely true, but none that are exploitable for this), I have no experience running a business, but I do have capital. And someone else who does have those connections and experience wants to start up such a business. Collateral on the loan protects my money (partially) in case of failure to repay, while the risk is mitigated by having someone more experienced doing the work.
Point being my rationale was slightly different; it includes more things - it's more general - and it's a bit more negative on the idea of simply buying a rent producing or appreciating asset.
The reason is: They don't need it. They want income, not assets.
Let's see, why doesn't Bank of America just buy millions of houses rather than lending out mortgages?
1. They don't need and don't have the manpower to maintain millions of houses.
2. Empty houses owned by the bank are not as valuable as houses with people living in them. If the bank owned every house in a neighborhood, nobody would want to live there and their value would drop.
3. They get to shift some of the risk to the person taking out the loan. If the value of the house drops, the borrower is still on the hook for paying the original amount (up to a point, unless they're willing to go through bankruptcy). So they don't get as much upside, but they have less downside too.
I'm sure there's other reasons as well.
If you're using it to buy an asset that appreciates more than the interest on the debt, what makes you think that you're a better judge of asset prices than the people lending you the money? Why wouldn't they just buy the asset directly, and cut out the middleman?
Businesses use debt for all sorts of reasons; cash flow, tax, paying out profits in a different form, or simply because debt is cheaper than equity.