Among other things, society will need more secure (truly malware-resistant) personal computing systems, more secure (from snooping) communications systems, substantially better authentication mechanisms, more secure energy generation and transmission equipment and facilities, more secure financial institutions, and more technologically-savvy regulatory and policing institutions.
Those are all really good things.
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[1] Compare, for example, how society works with paper cash and gold bars versus Bitcoin:
* Paper cash or gold in substantial amounts is always stored in private or bank safes, or in high-security underground vaults that most people have only seen in movies. In contrast, Bitcoin private keys are often stored in general-purpose personal computers running a wide variety of applications, managed by people who don't know how to secure a computer.
* Transporting any substantial amount of paper cash or gold is often done via armored trucks operated by highly-trained security personnel. In contrast, Bitcoin private keys are transported via all sorts of highly insecure methods by people who don't know better.
* No sane person holding a substantial amount of cash or gold at home would ever let complete strangers come and go into their house as they please, while giving them keys to all doors, cabinets, drawers, and safes. In contrast, people regularly give complete access to their computers to complete strangers by willingly or unwillingly installing software created by such strangers.
* Our regulatory and policing institutions know how to identify, prosecute, and even prevent illegal gold and cash transactions, successfully keeping them to a tiny percentage of overall economic activity in most advanced economies. In contrast, those same institutions do not yet know how to cope with the use of Bitcoin for illegal activities.
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Edits: moved comparison of Bitcoin to gold and cash to footnote; also, made minor changes to several sentences so they more accurately reflect what I intended to write in the first place.