It's not just time-value. It's also not just tying/advertising (although it is some of that - if I'm getting a ton of "free" points to American, I'm more likely to fly with them). It's both of those, and so much more.

Loyalty points work like gift cards in that huge numbers of them go unredeemed for any value, so selling them is just printing money. And unlike gift cards, which are typically denominated in currency, airline points don't have a fixed exchange rate to USD, so the airline can sell them to Chase or whatever for $0.01, and then if it needs to rebalance the books to shed the outstanding liability it can easily adjust the point costs of flights to make them only worth $0.009 - it's the same as a price hike, but in a way that's less noticeable to most customers most of the time. And that's assuming they don't just sell the points at an outright profit to begin with.

You can find a number of analyses showing that airlines operate at a loss if you set aside the miles-economy revenue streams. United famously got a line of credit secured against their loyalty program in 2020, in which they and their creditors valued the loyalty program at more than the value of the entire company of United Airlines - which would naively imply that the actual airline, the part of the company that owns large expensive machines and actually sells a product to consumers, had negative value.

Here's a longer overview with numbers and sources - https://www.youtube.com/watch?v=ggUduBmvQ_4

It's technically true but only because airline overall profits are really low. So you can pick any profitable corner of the business and say "the airline makes all their profit from branded toy lines" or what have you.