I don’t have an answer, but I suspect that spinning off the company is just a worse choice than keeping it or shutting it down. Maybe the same concept applies to IMDB.
Perhaps it’s the same reason why Netflix hasn’t spun off DVD Netflix. It’s profitable, but it isn’t attractive to sell to someone else.
I am just speculating.
BoxOfficeMojo by contrast is more like the old Alexa.com, it's almost worthless at this point. It has a bit of traffic they can use for marketing, so Amazon recently remade the product to update it a bit (first design update in like 12 years). Other than that, it's not very valuable.
It's an impressively dumb move that Amazon has made with Alexa.com. They should have entirely abandoned the name, when they went with Alexa for the name of their home consumer gadget product ('intelligent speaker'). They should have handed the domain to the new Alexa gadget product, so when consumers type in Alexa.com they get what they would expect to; and it should be marketed everywhere with that domain associated to the gadget.
Just rename the old Alexa web stats product and be done with it. If they think they can make some money off of it via AWS, that's fine, do it with another name. There's zero name value in keeping Alexa.com tied to what it is now. Call it the AWS Web Stats Service and hand Alexa.com to the AI product for consumers.