Looks as if it is a separate service on all platforms. I guess I can see why it make sense from both perspectives. Why couldn't it be one service across all platforms with one price, where each platform get's their cut and gamers simply get access to the EA games available to the platforms they play on? On the other hand, if that service needs to cost say $20 per month or $75 per year for multi platform, it makes sense to divide it all up and charge $5 for the month and $30 for the year per platform.
Still surprised there's little to no outrage by the cross platformers, but it would be directed towards EA and not PS or MS, unless they are a major part of the reason why the service is set up like that behind the scenes. We wouldn't find out either unless another Fortnite type controversy were to take place.
Almost all subscription services I can think of are platform agnostic and you pay for the subs itself. This is an odd and unwanted precedent.
I think, the reason is, that every platform has wildly different games.
The PS4 only has PS4 EA games
XBO comes with XBO and 360 games (do also OG Xbox titles get released with the service?), making it's offering twice as large as on PS4.
PC has the whole EA PC history, including all the games from PC-only companies like Bullfrog, Maxis or Westwood they bought up. It probably has a range of at least about 3 times as many games as the other 2 combined due to this.
In other words, you'll get by far the most out of it on PC, and on PS4 it has the least value if it has the same pricetag across all platforms.