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Upgrading from paper processes to computer-based systems is a huge leap, but upgrading between software versions may not provide an increase in productivity important enough to justify the costs involved. Having said that, the cost of keeping Internet Explorer 6 is high, and getting rid of it implies improved efficiency.
In-house written software that is only compatible with IE6 needs to be fully rewritten to work with other browsers. Sometimes the source code is lost, or cannot be ported easily. Microsoft did succeed to subvert web standards in the IE6 era. Now that has backfired. Poetic justice.
I don't see so much of a problem in having networked systems, since networked doesn't necessarily mean centralized.
Most sci-fi and action movie plots involving networks out there show an attacker going after a centralized system. They are assumed not to have enough resources to go after multiple independent systems. I've seen countless films where an alien force attacks us, we don't have any chance of winning, but then someone notices that the aliens depend on a central system. We defeat that system and win. Heck, sometimes it goes so far as having all attackers die on their own after their mothership is destroyed.
I guess most first-class military strategists understand the danger of having centralized command-and-control systems. I don't think we must give up networks. Cylons in Battlestar Galatica were essentially machines. They had optical fiber running to their nervous systems, and their minds could be linked to computers directly. Not having so many interconnected systems with such an enemy was a very sensible choice for them. Not so much for us as we generally need to defend only from other humans.