A compose key is very useful if you’re a typography snob — as many of us who studied mathematics and ended up learning TeX probably are… I haven’t been paying attention to exactly what I’ve typed with it lately, but I habitually use symbols like these on autopilot and they seem to render OK on any device that someone reading my writing is likely to be using:

≤ ≥ ≠ × — – “ ” ’ ° … ¹ ² ³ ™ • ♣ ♢ ♡ ♠

If you work in languages other than English but have a standard English keyboard layout, a compose key is handy for typing accents and non-English letters/ligatures too.

I primarily work in Danish; but I use a US Intl AltGrDead[0] keymap, so I can access most needed symbols without the compose key, such as æ (altgr+z), ø (altgr+l) and å (altgr+w). But I still wanted to write ⅚ more easily, so I also added the compose key for even more symbols.

[0] The AltGrDead variant just means that the regular dead keys on the US Intl are flipped; e.g. ' is now no longer dead per default: I have to hit altgr+' to make it dead (i.e. an acute accent (´)).

Oh yes, compose-key is great for the occasional German, but even for my native Dutch it is useful — not to mention Frisian.

See also :

https://norme-azerty.fr/en/

(Also provides access to the Greek alphabet.)