I'm not a programmer or an engineer, so please forgive me if any of this is misinformed, over-simplistic, or just plain stupid.
The difference between pre-Y2K and today is that a programmer is less likely to hard-code limitations into critical software -- they'd be in subroutines or at the OS level, making it much easier to update or port a program than it was with the old, patched to the Nth degree, and mostly undocumented COBOL and FORTRAN code.
Another difference is that we might have actually learned from y2K (stranger things have happened), and databases have come a long way. If the critical data is stored in some standardized form, it would be a lot easier to move to another program or platform, even running the old and new systems in parallel to make the switch smoother.
And finally, virtualization is a pretty mature technology. It's easier now than before to run old software in its own little sandbox while making a transition to the new hotness. Bringing it back to Apple, this is something they're old hands at -- 680x0 emulation on PPC, PPC emulation on Intel, and Classic on OS X all made those transitions shockingly smooth.
What it means is that your son could very easily see the time when an unnecessary software limitation creates a crisis in the operating system. Which, looked at in that way, is pretty optimistic after all. Why would OS X necessarily last two human generations?
I guess my point is that it's a lot more modular than it used to be. OS X might not be around in two generations, just like few modern-day admins have even seen the big iron the Internet was built on. But TCP/IP survives, and if you get a couple of beers in a cranky old-timer, he'll start ranting about how "Web 2.0" is really just telnet 5.0, or gopher with pictures. Or, for that matter, that it's all just an extension of the telegraph, which was a packet-switched digital network before the telephone gummed things up with all that analog stuff.
They do it all the time. Take for example using an integer (signed, from -2 billion to +2 billion) for an index of records, very common. Then you find out your application is much more popular than expected and you're about to run out of numbers for the index. You then have to change them all to unsigned integers to get 4 billion records, or to unsigned longs. With the latter you get about 18 quintillion, effectively unlimited, but you never thought to do that in the beginning because that takes up twice the memory when processing and twice the space in the database.