Given that most of this code was originally targeting systems from the 1960's and 70's, I can't imagine there being an insurmountable number of lines of code
According to Wikipedia, Gartner estimated about 200 billion lines of COBOL code in 1997. To put that in perspective, that's more than the total amount of open source C code tracked by OpenHub.net. Can you imagine persuading someone to rewrite all of that C code in a newer language?
A quick google search shows that there are, by the most wild estimate, 600 people on the planet, at most, who are over the age of 110. More like 150 to 300.
Raising the age to 130 just means there's an extra 20 years of potential pension fraud or incorrect payments.
Why would someone who is not a programmer set up such an arbitrary limit?
Probably because it's not arbitrary; most people don't live to be 110, and everybody knows you're supposed to perform sanity checking. According to a quick google search (the height of scholarly rigor,) there's maybe 300 people in the world who are older than 110 years. The most wild estimate is 600.
On the other hand, fraud is a real thing, not to mention straight up human error; somebody dies, they don't get taken out of the system, so the money keeps going out.
I doubt very highly it's a 'two digit year' storage issue.
More likely, it's perfectly correct and reasonable boundary checking; an age should never be less than 0, and never more than, what? How many people are actually older than 110? She is an extreme outlier, and proof positive that the boundary checking is working.
Then, almost by definition, it is worthless
And yet it works in exactly the way Libertarians are telling us things will work: companies put an agreed-on label on their products, they have an incentive to check unreasonable-sounding claims from their competitors as do consumer groups, and there is redress through the courts (and bad publicity) if anyone is caught cheating. For once, it's a free market solution that is working with a minimal amount of government intervention.
This isn't the reason the cloud makes a terrible backup. The thing that you want to avoid with a backup is correlated failures: things that cause a failure of your primary store should be different from things that cause a failure of your backup. Your house burning down or thieves coming and stealing your computers will cause failures of both your original and on-site backups. It's a lot less likely that the founder of your cloud provider will be arrested for the same reason that you lose your laptop.
Remember: it only matters if your backup storage fails at the same time as your on-line storage.
You can address that by having a progressive tax. In the UK, there are tax-free savings accounts that have a limited pay-in amount per year, income on which is exempt from income tax. You could do the same thing with a wealth tax: anything in a tax-free savings account doesn't count. You could perhaps also add an exemption for money in your primary residence, up to the median house price in your region. Beyond that, add a tax-free allowance of something like $50K and most people will pay nothing.
The real problem with such a scheme is that it's open to tax avoidance. It's fine for poor people, whose wealth is typically in cash form and so easily valued, but what about wealth held in private stocks in off-shore corporations? Those currently don't even need to be disclosed, and if they are then it's often very difficult to determine the value of the company (especially if it's a shell company that owns other shell companies that own real assets, with arbitrary levels of indirection in the middle). To make it work, you need complete financial transparency on all private companies.
 When they were introduced, this was about £3K, which was pretty reasonable. If you're earning 50% more than minimum wage in most of the country, you can get close to this. Now it's over £10K, which effectively makes it a tax break for the rich. Unfortunately, it doesn't roll over either, so if you have irregular income then you couldn't put in nothing one year and then £6K the next.
A list is only as strong as its weakest link. -- Don Knuth