See now, I believe this will be the opposite. Netflix is going to be scrambling for customers when Disney+ launches. In fact, Netflix most recent quarterly results stated they only added 2.7 million customers last quarter, which is half of what they and the industry forecasted. Netflix saws its first major loss of subscribers and about 2.7 million less than anticipated (that's a huge blow).
Disney+ already stated that you will be able to get Hulu, ESPN+ and Disney+ for $12.99, which is the same price as the Netflix Standard plan. You can get Disney+ solo for only $6.99, which is $2 less than the entry level price at Netflix.
Competition is always good for consumers. The next couple years all the media companies are going to push towards this digital distribution model. When the dust settles and only a couple of these platforms remain though, then pricing may not be consumer friendly. For the next year or two though, everyone will price competitive to try and get you to try our their service or flip to their service.
I'll be happy when the physical cable boxes go the way of the pay phone and just disappear forever.