I'm totally not qualified to talk about this, but since I'm just writing an off-the-cuff comment on a website, I can at least give you my impression. Don't take my word for it, I'm probably full of shit.
Keep in mind that the debt here means that depositors gave them money in the usual bank arrangement. When you deposit money with your bank, they don't let the money sit in a physical vault or the digital equivalent. They put as much of it as possible to work. The Icelandic banks had used the money to make diversified investments across Europe. I'm from Denmark, and in this period there were several noteworthy Icelandic investments in major Danish companies, and that was the pattern all over northern Europe. It was a far more responsible and effective investment strategy than what was generally followed by the Irish banks, who injected the bulk of their investment funds back into the Irish economy, especially in the real estate market, thereby artificially inflating and extending the Irish bubble.
> I realize it's not easy to see the forest from the trees, but isn't there some point at which banks start to see that they are taking on too much debt?
They could have hedged against overall market drops much better than they did. They put too much into real estate. Etc. But when there is a rapid and systematic dive in confidence and all your major depositors make a simultaneous run on the bank, you are pretty much screwed. They'd have needed to bet a sizable chunk of their funds against the market as a whole to cover that eventuality. But if everyone had done that, things would quickly have gone nonlinear, so it's unclear at least to me what they should have done, given their mandate to invest the money on hand.
The root mistake was probably taking on too many easy-come, easy-go customers who'd want to make a quick escape in the event of a down-turn.