Also remember that even VISA, the largest transaction processor in the world, only averages like 3000 or 4000 txs/sec. So while the LN may be able to technically handle on the order of 1 million txs/sec, it will never get close to that number
It can easily get to this number and VISA is not the right example here. LN can handle billing for pay videos, phone calls, ect. on pay per second level. VISA cannot do it.
Easy to get to a level of 250x or more what the largest payment processor does....that's not easy. It MIGHT eventually happen if micropayments take over for a lot of stuff. But for most things micropayments are not a better solution. Subscription services are a lot better for a lot of things and will never switch to micropayments, because with subscription services you know exactly how much you will be paying, and can get a better deal if you use it a lot, which you probably do if you find it worth paying for, and the company knows exactly how much they will make as well, so for many services the subscription model is much better both for merchant and consumer. Your specific examples for the vast majority of people work better as a monthly subscription service.
No doubt some new kinds of services will spring up around the micropayments option, but to say it will easily go to 1 million tx/s is right now pure fantasy.