I don't think that everything he touches "is shit or turns to shit quickly". The Apple Online Store, iTunes Music Store, iCloud services, Apple Pay are all great products/servives. He took command over Maps when it was at a terrible stake, and it has improved a lot since.
However, I think iTunes, Apple Music and Siri all have weaknesses. But we can only guess who's fault that is - certainly not Cue's alone.
Also, he is employed by Apple since 1989. He must be doing something right.