I suspect that, in many cases, AI features actually make a product more expensive for the operator. Imagine how much of doordash's money you could burn by telling its chatbot that the only way for you to figure out where the driver left your order is to create a todo app in React.
Everyone would prefer a nicer handmade chair (if not by the price difference).
Chairs are not comparable to OPs cards; writing on a card costs nothing (but intent, which seems to be in low stock these days).
Finally, factoring in the real operating cost, ongoing capital costs, and environmental/social externalities, the AI chair in your example would cost something like 1000x a handmade chair.
One is the method of recording a message, the other is having something else completely draft a message for you.
The importance of a personal message is not just in the visual appearance or delivery, but that there has to be some emotional loading to even put the effort into drafting one.
With AI, it's a stupid prompt to get it to write trite poesy. It's meaningless and empty at its root. It's discourse with a nullity.
Nobody who values the human connections in their lives wants that. No matter what kind of marketing and fine print gets shoved and manipulated into their lives.