I think they'll be OK this current price increase, but not the next one. I'm sure they have a good model on cancellations after price increases and they'll make up for the loss with the increased price. But I think a lot of people are going to start examining if they want to continue paying for Netflix every month without thinking. More people will likely cancel and re-subscribe periodically when they hear about a series or movie they want to watch. And the more competition from other streaming providers, the more people are going to be examining their total spend per month on streaming services, which if you have a lot of them, is beginning to approach a traditional cable television bill.
The price increase really wasn't the main driver for me; it was more that Netflix continues doing the exact same thing -- manipulating its users through user interface trickery, and continuing to spend money on content that is not very good. The more shows, including original series that I pass on, the more I realize that I'm paying an increased monthly cost to finance Netflix's overspending on B-rated content that I won't even be watching.
I also think Netflix took away the wrong thing from the Bird Box "success." Yes, a large percentage of Netflix subscribers watched at least 70% of the movie, but I think it was 1) to see Sandra Bullock, who is a great actor and 2) it came out over the holidays when you often want something in the background to watch because there isn't a ton of things to do that the entire family can do together. For me, I'm a fan of Sandra Bullock so that is why I watched it, but the rest of the movie and story was not that great or anything unique.
After I cancelled Netflix, I signed up for YouTube Premium instead, and I feel much better about it. You can turn off auto-play and video previews don't have sound. YouTube music isn't quite there yet, but it's getting better, and the iOS app is solid. And their recommendation engine is actually good. Plus I like that I can watch ten or twenty minute videos on an infinite variety of things instead of committing ten hours of my life to a Netflix show.
If Netflix had any faith in their own content, they would introduce some kind of impartial review system (either user-based, or Rotten Tomatoes, etc). Netflix's "% match" system is a complete joke; I frequently see 90% matches and start watching and go "why in the world was this recommended to me?"
Disney will also be launching their streaming service this year, and it will be rumored to undercut Netflix pricing. Plus Disney will now have all the Fox content, some of which is on Netflix and might be pulled down the line. I think Disney+ will also be more appealing to people with kids over Netflix, which tends to be more adult-themed.
The other issue they're going to run into is that they have almost reached peak saturation in developed markets. In order to continue getting new users in developing markets, where those people will be more price sensitive, they cannot keep raising the price. I wouldn't be surprised if they begin segmenting the pricing by region, or creating lower cost plans that only have limited content, or more restrictions.