A subscription fee for their entire catalog seems like a good idea, in theory. The problem I am seeing with it is bandwidth usage. Observe;
You pay your subscription, download and play. Finish playing and the game deletes itself, you are (essentially) renting it remember (most likely after a set period of time, 24-48 hours maybe?). Now while this may seem like a fairly big assumption, keep in mind this is EA here.
Now to circle back to my starting point, bandwidth usage. The average data plan is, what, 300gb? With games clocking in at around 20-30gb installs means you will burn your entire allotment very quickly.