As Bitfinex, the digital-currency exchange that suffered a hack this past week, struggles to reopen, a wider question is again being asked about bitcoin: Is it really a better mousetrap?

On Tuesday, cyberthieves stole about 120,000 bitcoins, valued at roughly $65 million, from Hong Kong-based Bitfinex’s digital vaults. It was one of the largest hacks in the currency’s history.

Bitcoin...