That argument doesn't really work as well as you think it does when you actually know you're paying for with a PSN+, XBL, NSO subscription. You're not paying for general connectivity (thank god), you're paying for the privilege to allow your online ID to be used for match making. Video streaming services obviously don't make use of your gaming account at all, so it makes sense they're not affected by the paywall (and the same is true for games that use their own account system exclusively, like MMOs) but F2P games do use your online account for match making just like most other games, so them being exempt from the paywall could understandably be seen as an oddity.
The reason Sony (and may be Nintendo too) grant F2P games an exemption is because the paywall is pretty much bullshit in the first place (they're not covering any additional costs that don't already apply to non-paying accounts too, it's practically pure profit*) but they know that allowing F2P games to be truly free to start is a better business practice, so it doesn't really hurt them to make an exemption. The whole reason the F2P model works is because by having no upfront cost they can attract a lot of players who would otherwise not be interested to at least try the game (and from there some of them can be hooked and made into paying customers). Putting F2P games behind the paywall wouldn't be an issue for those who are already subscribed to PSN+ already but for those who aren't, forcing them to pay out of pocket for a subscription before they can start playing kind of breaks the business model. It's not a pro-consumer policy, it's a pro-publisher policy that happens to be mutually beneficial for consumers.
*To be fair, you could argue the subscription works the same way F2P games do, where the paying customers are subsidising the free-users, but still, even accounting for that overhead, I'd wager that the profit margin would be ridiculous non-the-less.
