To reap the benefits of compound interest (in your favor), you need to stick to a plan. You can't dump your investment portfolio after 5 years. It's these small, daily decisions that add up over time. So while the output is multiplicative, the necessary input is only linear.

Yes but the linear input is not the relevant part. The compounding is.

If you had to put in compounding effort, the compounding output would seem far less intriguing or worthwhile. If investment returns weren't exponential, or required exponential input to receive exponential output, it'd be far less useful of a concept.

The word 'add' is overloaded for both mathematical and non-mathematical purposes.

Multiplication is just a specific form of addition operations and is easily writable as such.