What Apple Music has that no one else has
''Apple is leading the digital music revolution, but at its core its all about music''
Apple has one major thing over its competitors - a LOT of people's credit card details on file. In 2014 it was estimated that this was over 800 million - iTunes Has 800 Million Accounts.... and 800 Million Credit Card Numbers... - Digital Music News - which makes it easy for them to turn new services on like streaming and monetise it quickly. They can email those users, and at the click of a button they can subscribe. Competitors do not have that luxury! That was how they managed to attract million of paid subscribers so quickly when Spotify has taken much longer to achieve their growth
Spotify has has about 15 million paid users. That may sound like a lot, but that's tiny compared to the actual market. Not only do they pay artists only a tiny amount for their music streams, they make no profit as a company and have no clear way to make a profit. Spotify will either have to dramatically change to start making money or they will be bought out by a bigger company who doesn't mind losing money to attract costumers. Additionally, artists and the music industry don't like Spotify. They tolerate it because they don't want to alienate customers. Tidal and the other streaming services have similar problems. Not paying artists enough and not making any money. Big companies like Apple and Google are going to be able to absorb these losses because they gain them customers. Apple doesn't care if they lose a little money on a music service if all of those people buy iPhones.
Tidal appeals to a niche who wants the exclusive content and high quality lossless compression. Most people don't care. The T-Mobile deal you mentioned won't last and may violate Net Neutrality so don't hold out that you'll be able to do that forever.
What does Apple Music have?
Well they have a plan to pay artists fairly well, something only Rdio has done.
They have a strong brand and a global, successful business that is making a profit, meaning that people don't have to worry about them going away.
Most importantly, they have 800 million iTunes accounts. That's mindbogglingly huge and more accounts than Amazon has. If just 10% of those people sign up for Apple Music, they'll have instantly dwarfed every other streaming services paid accounts combined. 10% is a fairly conservative estimate as well.
They also have exclusive content and are likely to get more as artists that have withheld their music from streaming services in the past are allowing it on Apple Music.
Apple entering the scene and at least matching the existing services changes the entire game. Spotify fans will likely stay with the company but growth will slow. There will be more pressure from the music studios for services like Spotify to drop their free services and do a free trial like Apple is. Eventually they'll likely get scooped up by another company or change to the point where they won't be recognizable as the company they are now. Look at Hulu for an example of an awesome service that is now terrible because it had to start being profitable.
You're looking at this from your perspective and from just a consumer perspective, Spotify and its rivals are great and Apple Music is late to the party. From a business perspective and from the artists and studios perspectives, this changes the whole game and consumers are just along for the ride. However, don't worry, it will be a good ride.