I think part of the reason this question gets asked so often is that there are people who complain about DLC elsewhere then they turn around and defend Amiibo. That's not only hypocrisy, it also creates a target for criticism. In the console wars, it results in an opportunity that would equate to a bombing run or an artillery barrage.
Of course, sometimes the question is genuine or comes from a real desire to debate the topic, and you also have people who are honest about their criticism/frustration with the hypocrisy. Not everyone is painted with the same brush.
Personally, my only problem with Amiibo would be if it provides extras that you cannot get elsewhere.
As an example, let's say that I really want one of the Zelda Amiibo DLC functions and it turns out that I cannot earn that function in-game. However, I have zero interest in collectable toys. If I were going to display something gaming related--and I'm probably not--I'd buy something nice. That would make the DLC both overpriced and inconvenient to use.
That, to me, would be an annoyance and a betrayal of the non-toy-buying fans. Anything available using Amiibo in a non-Amiibo themed game should be up for digital purchase. I think that would remove most controversy. The exception would be games that are centered around Amiibo from the start, as you should expect to need Amiibo for that.