Terminfo goes back to the early 80s, during the time of the Great Unix Wars when everyone was doing everything different for the fun and sake of it. It contains a lot of cruft. People are mentioning ADM-3A terminals here and that's all very nice, but these are machines from the 70s. No one is using them, except some people for the fun/historical value. Do people write software to be compatible with Bell Labs Unix from 1976 or 1BSD that Bill Joy was working on? Of course not.
AFAIK there are very few modern terminals (or rather, terminal emulators) that don't support that basic set of escape codes. I can't really find any in a quick glance at my system's terminfo database.
For basic operations it's pretty safe to rely on, at least if you care about Unix only (not entirely sure about Windows, I believe it's all different there). Once you go beyond that it gets a bit more iffy.
There are loads of programs that hard-code these things, including very popular once. The issue trackers of these projects are not getting filled with people reporting garbled output.
[1]: https://www.ecma-international.org/wp-content/uploads/ECMA-4...