I don't really buy into the knock-on effect. I do think that if a game is cheap, people will buy. The Trilogy has sometimes been sold for what, $15? $10? And *gasp* it sells at that value? It shouldn't be a wonder why.
Nonetheless, when a new iteration, let's say Saints Row IV, for example, comes out, people who haven't played the previous games do buy them, and play them. And so dropping support for them immediately, or even any time soon, after a new release is a bad idea, and the big publishers know that. Some are so canny that they make extra money out of it. The online price of Black Ops I actually went up after Black Ops II was released because Activision knew that many people would play Blops2, like it, and want to play Blops1. Ghosts was put back up to full price after Advanced Warfare released as well. To go back down the line, as far as I know, Activision has kept the MW2 servers going to the present.
And yes, EA could put ME3 on the house, it would keep interest alive for ME:A. Not long after BF4 was released, they put BF3 on the house for a couple weeks, so people would get hooked and buy BF4, and it worked. They kept the BF3 servers running though. And that costs a lot more than the ME3 servers.
It still comes down to this question: why are you so convinced that EA will think it's a good idea to shut down the ME3 servers when ME:A is released? They know everything that we've discussed on this subject, and they know that shooting a valuable franchise in the foot is not a good business idea. So why do you so strongly believe that they will do it?