> Why should the future of internet streaming be DRM free?

Because there is no good reason to use DRM. Ever.

> But for streaming video I'm merely renting.

You mix up the concept of streaming with renting. A common mistake that for some reason a lot of people make.

Streaming is simply a convenience. An ability to watch something from the cloud without downloading it first. Who said it has to be equal to renting? You can perfectly buy something and have it stored in the cloud to stream it while being able to save it for local backup at the same time. That's exactly what GOG offer for their DRM-free video.

Now with streaming misunderstanding out of the way let's take a look at renting. First of all using DRM for renting is pointless. If it's intended to prevent potential abuse of renting terms, then it's worthless same way it's worthless to prevent any piracy in general since those who want can access all the same content through piracy sources at any time. So any kind of enforcement of renting with DRM is futile and only reduces usability of the product for nothing.

Now let's also review the concept of renting itself. It doesn't really make any sense for digital goods in general. For physical merchandise renting allows reusability, which allows in term using lower price for renting in comparison with selling since there is no repeated cost of production. For digital goods this problem is non existent because cost of reproduction is practically non existent (digital copying). So there is no good reason to make the price of selling any higher than the price of renting. Or in other words, the whole concept of renting is nonsensical for digital goods. It wouldn't hurt to always allow the user to back up their data if they want to (i.e. complete purchase, not a rent).

Now with renting out of the way let's take a look at Netflix. Essentially their novelty is not in the renting aspect, but in an interesting way of organizing the service. Instead of selling film per price, they give access to anything for a monthly fee. This can perfectly be done without falling into renting approach (which can push one to entertain the thought of DRM which is nonsensical anyway as above). Some say, that if you remove DRM from Netflix what would stop users from downloading the whole catalog within the monthly period? The answer to that is that DRM is still not needed, Netflix should just make terms of usage more realistic and use other, non DRM methods to prevent such abuse. I.e. instead of saying "watch what you want in any amount by paying N money a month" they can say "watch / download up to M films by paying N money a month. If you want more - pay extra". That would keep basically similar approach but would prevent potential "download it all" abuse, while at the same time remain DRM-free. And there is no need to turn it into renting. I.e. those M films can be made perfectly downloadable and backupable. Since the main expense for Netflix is the streaming (it eats bandwidth / server activity resources), letting users back video up is perfectly fine - it will only reduce costs by reducing load if users will decide to watch their local backups next time.

The bottom line, Netflix can offer a DRM-free streaming service which allows downloads at the same time and uses their approach of "watch what you want for a monthly fee" except with an addition of "not more than M videos per month. If you want more - pay an additional fee".