Why not? I mean sure, it would mean losing the anonymity, but the receiver would owe you the interest-adjusted amount just like someone you lent money to. A loan isn't magical boomerang money, it's a legally encumbered transfer, which can be done with dollars, bitcoins, tractors or anything else.
In fact here's bitcoin lender right here: https://www.bitbond.net/
Lending -- as an institution, as opposed to as an individual -- is all about fractional reserve banking. The bank pools the money of its depositors and lends it out without restricting the ability of the depositors to access their money. This increases the money supply, and generally works OK because of a combination of (a) most people not needing most of their money most of the time and (b) a lot of transactions happen purely through the bank's internal ledger, without needing cash at all. If Alice writes a check to Bob, who immediately deposits it, the bank just updates their ledger and it doesn't matter whether they have cash on hand to cover it.
There's nothing preventing you from operating a traditional fractional reserve bank using Bitcoin instead of cash, and it would work the exact same way as a traditional bank with exactly the same advantages and problems. But if you're writing checks for Bitcoins instead of dollars which end up being processed entirely through a bank's internal ledger instead of through the Bitcoin network's blockchain... why? How is that really Bitcoin?
The problem with the more vociferous proponents of Bitcoin – and not only Bitcoin; you can see the same thing happen in the tech industry in discussions of women or minorities – is one of politics. The problem is this: many in the American tech industry don't know what politics is. According to Wikipedia, it "is the practice and theory of influencing other people on a civic or individual level;" it's a general term for managing powers and spheres of influence in society. Worse, they seem to shun it.
But politics can't be avoided. It is essential to human society. When people shy away from politics, a dangerous thing happens: they practice bad politics based on naturalistic fallacies. I think science oriented folk are particularly prone to that because science concerns itself with what is, while politics concerns itself with what ought to be. Science people might, and do, come to believe that what is, is what ought to be (or the only way to be).
In fact, Bitcoin is a very interesting example because it allows (actually, it is only imagined to allow) removing people out of the equation altogether, leaving algorithms. When you take power away from people and put it in the hands of mathematics you indeed lose politics (except, of course, for the original act of seizing that power). But then you lose a lot of what makes us human.
I think that there is in Bitcoin a confluence of tech people falling into naturalistic fallacies with a general lack of trust in institutions that has possibly been growing of late among Americans. It is interesting to watch, but the arguments, unfortunately, are no different from the old American-libertarian anti-government, pro-gold, arguments. The difference, this time, is not in political awareness (of which there is a dire lack), but in – here's that word again – power. American libertarians traditionally had little power. They have been a small minority of both the general population and even of the rich and influential. But now technology is not only a power (which it always was), but one with exceptionally low barriers to attain. Bitcoin supporters, by virtue of their part in the powerful Silicon Valley sphere of influence, actually do carry a not-insignificant political weight. This will be interesting to watch.
Whatever happens, even those who believe in institutions should welcome this challenge, because democratic institutions always benefit, in the long run, from worthwhile challenges. So far they've shown an incredible ability to adapt (though the rate still appears too slow to humans who only live about 80 years), and there's no reason to believe they will not evolve for the better as a result of this interesting challenge.
It is interesting to watch.
Sure banks fail and make mistakes but the FDIC has kept small depositors from losing all there money for a long time. Computers are hacked or mess up all the time and with Bitcoin such issues are unrecoverable which makes trusting computers seem like a terrible idea. For reference 1/2 the people I know had there WoW account stolen and that's worth less than 50$, if significant numbers of people where to try to hold significant amounts of bit-coins directly you could expect similar things. Right now bit-coins are small enough and fractured enough not to be a useful target but it just does not scale without 3rd party institutions.