Not true. Indeed, very much the other way around. All software that uses the terminfo or termcap databases looks at the TERM variable and gets the TERM=dumb effect from that for free. That's every shell script that uses tput to change colours, and every program that calls the low level tgetent()/tigetstr() (or the equivalents in unibilium or termdb) or that uses curses/ncurses.
This is a wide range of softwares from the %F and %B sequences in the Z shell's prompt through Midnight Commander to the clang++ compiler.
You've clearly either never looked at much doco or have a truly terrible memory. In addition to all of the books and whatnot over a span of 40 years, even The Linux Documentation Project got in on the act: https://tldp.org/HOWTO/Text-Terminal-HOWTO-8.html#early_term...
Most of the software that outputs colors are scripts or CLI programs that use hard-coded ANSI escape sequences, not termcap or those library functions.
You haven't measured it, and the large number of questions and answers on just Unix StackExchange, without checking all of the others from AskUbuntu to SuperUser that are like https://unix.stackexchange.com/a/327544/5132 indicates that yes, people do use tput in scripts as a matter of course.
Almost all software that outputs colors only checks if the output is a TTY and doesn't look at the TERM variable.