I'm interested in starting a subscription box business but the current market seems so saturated. There's basically a box for everything already.
Depends. I think the broad level is saturated, but cutting into a market's subcultures is where it is at.
I did a FREE makeup box, just pay to ship, in a saturated market and had huge success at around 20k MMR within 3 months because we targeted a submarket.
I think it is more finding a niche of a niche now to be successful in sub boxes. A good example would be like vegans. There are meal boxes and treat boxes for that community and do well. Maybe find something within that community no one is doing like vegan accessories, vegan apparel, vegan {insert here}
My (limited) understanding is that success with this business model depends on finding an underserved niche.
It's not "is the subscription box business model dead?", it's "is a subscription box for <hare-brained niche idea> business model viable?"
As an example: Is the restaurant market saturated? Why would anyone open a new restaurant?
The margin might be low, competition fierce, but you can always find space for your product with innovative positioning and marketing.