Earlier quoted context omitted.
I think you're overlooking the "on their own" part. The OP isn't lamenting that things are less reliable in general, just that they aren't reliably capable of working offline or on a local network. Phones are maybe an odd example, but it's somewhat true: Traditional phone systems let you make local calls even if long-distance lines fail, or within a building without leaking data externally. Very few people would ever…
I don't think I've ever heard a fast-busy signal from my cell phone, even once. But it happened lots with landlines when too many people were making local telephone calls. Circuit switched networks kind of suck in a lot of ways. I don't think I would say traditional phone systems were as reliable as modern telephone and data systems.
And personally, as someone who grew up in the 80's, let me offer up a counter-anecdote: I don't ever recall hearing a "fast-busy tone". There was never a time we couldn't use our land line (at least until we had a modem, that is).