The term addiction is commonly used to describe something else though.
Addiction for the most part is life shattering and not about 'having headache for a few days when not drinking coffee'.
Sure, withdrawal effects are a criteria for substance use disorder and I guess you could construct a mild disorder by finding some other criteria.
But nobody becomes homeless because of coffee consumption, nobody loses they job or friends because of it, nobody smokes or injects caffeine to have a greater effect.
You can call people drinking coffee addicted, but that only works for the effect because addiction is a terrible disorder, not because coffee consumption is that terrible.
Btw: I consume products that contain caffeine very rarely (1 per month maybe).