are you saying it’s because a daily doubling is itself exponential

Yup, that’s what I’m saying! I’m not the kind of person who will get on someone’s case for using exponential colloquially to mean “growing really fast”, but when you explicitly describe an exponential function and then imply that it’s not exponential, that’s just sloppy. Bringing in nonlinearity, which makes it seem like you’re being more mathematically formal, makes it even less acceptable.