If Israel went forward, the currency would unsurprisingly be kept on a tight leash. It'd be centralized, "safe" and honor financial rules. Don't expect the country to simply adopt bitcoin and call it a day.
The bank has declined to comment. However, it's easy to see why Israel might at least be tempted by cryptocurrency. As the technology relies on blockchain, where there's a distributed ledger that can quickly verify transactions, you could see payments fully authorized and completed within minutes no matter when they're processed. You wouldn't have to worry about paying a bill on the weekend and having to wait days before it clears.
This isn't a guaranteed solution. Israel would have to convince residents and businesses to use this currency. There's also the not-so-small problem of whether or not the currency would be useful with international transactions. Even so, it's notable that Israel is even mulling the option. It's looking at cryptocurrency as a practical solution to an economic problem, rather than an experiment or something to be shunned.