It might need to be $40/m to be profitable on the marketing. Now add in the extra resources to sell direct content access, price for the fact that the market is vanishingly small, and it could easily be 10x the price. Would you pay $500/m? Now it's so expensive you're way more likely to churn, and actually they need to make back money much quicker to sustain it. Would you pay $2000/m for Netflix? What sort of experience and support would you expect for $2000/m, now Netflix needs a new sales and support org, and it costs a huge amount to keep them around. Would you pay $5k/m for Netflix?
Obviously these numbers are all entirely made up, but Netflix is built on a large subscriber base and very low touch sales and support, with expensive engineering amortised across hundreds of millions of users. All that works in the opposite way, so I don't think these numbers are the wrong ballpark.
There aren't many people who would pay $5k/m for effectively the same service as they can get for $20/m.
In this way it's all quite different to my TV example. There you're paying $500 for a $700 TV because they'll make $300 from you on average. Just not including the smart TV functionality might only cost a little more, and then the TV might sell for $1k and a fair number of people would buy it.
But as you said, you completely made up that number. You could just as easily have made up the number $20.01.
Note that the provider of this UI would be bound completely to the terms dictated by the streaming service(s). E.g., it might look interesting to have all your streaming services in one app, but Disney or Netflix or Amazon or HBO can simply forbid that option.
Something I would gladly pay to live without.