The answer as I said in the post preceding yours is to use a similar app such as the Onkyo HF Player (which is free) which has crossfade although it is not adjustable but works well. I'm sure there are other similar apps.
What you're describing regarding the computer/laptop has not changed as the current Music app for Mac computers has crossfade as did all iTunes Mac/Windows versions. The iPhone/iPad OS is different then Mac OS or Windows although with current Mac OS, there is a closer integration. Why the Android version has it I can't say. As for the first iPhone which I still have, it did not have crossfade on the iPod app which was what it was called then. This is why I have used the Onkyo app when I bought an iPhone 4 since iTunes/iPod app never had crossfade for the iPhone and I assume iPad which I do not have. So you are incorrect about the first iPhone which is understandable as I had to turn mine on to be sure as well.
I would look into an app which has the features you want since it does not appear that the newer Music app is going to be any different than the previous iTunes iterations for the iPhone or iPad.