And then there's the whole he's in the middle of a conversation with someone right now? It would be rude of him just to ignore her and go straight for the phone.
But, if you can give me even a single non meta-gamey answer to wait, I will change my mind.
Alex just learned he slept for four months after taking what appears to be a miracle drug that cured his cancer and in the same moment, gave him absolutely terrifying superpowers. If he calls them what is he supposed to say? "How do I tell them that I basically just drank a strange liquid handed me by a strange woman on the off-chance it would cure me? That I essentially risked the last 3 months I had to live?" These are terrifying questions for a young man to even answer to himself let alone to his family.
No metagame answer needed.
Or at least to procrastinate it until such a point where we would be given a cover story.
As much as I love the discussions going on, don't get me wrong they are fantastic, but I feel the need to remind people of one important fact.
I will ask you this, where are you?
You're in Cauldron, the organization created for the preservation of humanity at any and all costs.
Alex is capable of Controlling
Gravity, and that's only one of the powers that the Intensity shards give him.
To quote the good doctor:
"Subject has confirmed to control one of the fundamental forces of the universe. Inform Doctor Mother, another deterrent has been uncovered."
As of right now, Cauldron has created three Deterrents. People capable of fighting the true challenge, Scion.
At this point, Alex has the potential to be the third most powerful being in existence. Cauldron knows this,
Contessa knows this. She is under orders to insure Alex's support. She has made sure, that everything goes according to Doctor Mother's
Now I ask of you, how much would Cauldron manipulate events, set things up, so that this deterrent remains with them?
Support structures are certainly a necessary component of what we're going to have to develop to keep Alex from going insane or turning into what we saw of canon Alexandria(aka a walking, breathing automaton).
On that note, we should also remember that Alex is Rebecca's support here. She has been awake most of those four months and she didn't contact her family. We have a rough idea that she isn't terribly happy with what remains of her home life and looks to Alex's family as a substitute for her own, with Alex as the primary point of contact.
We know what she turns into in canon; lets avoid that.
Actually, to answer this for the thread, the amount of times that Rebecca has even thought of calling her own family is exactly zero. She has never once thought of giving them a call.
In fact, the only people she has interacted with outside of Cauldron for the last four months is Danah. Officially, unlike Alex, Rebecca didn't fall into a coma due to the treatment that cured her. She was the one that called Alex's family to tell them about his situation. She was the one who gave them the numbers and the express information about Alex's condition. She gave Danah hope, but only confirmed what Clint and James feared.
Had she not done anything, Alex and Rebecca would have officially been listed as dead and Cauldron wouldn't have told the families anything. They would have made puppet bodies, they would be buried, and their original lives forgotten when they became heroes. The families are irrelevant in Cauldron's eyes, only the deterrents and the heroes are what matters.