terminfo has not died. M. Dickey made updates to it last month.
terminfo's problem is that it is really difficult to make changes that extend or do not fit the original paradigm, not least because the actual database format does things like have a fixed set of implicitly-named boolean capabilities, with any additional capabilities having to be named 'extensions'.
* https://github.com/mauke/unibilium/blob/master/secret/termin...
But other problems include terminfo's model of how things work, such as function keys for example, not really matching how they actually work in terminals and terminal emulators. For function keys, for example, DEC terminals allowed modifier state to be sent in parameters to DECFNK. terminfo's design had no concept of this.