UPDATE
So I scheduled a call with Apple Support on October 10th for this issue. After speaking with 2 customer care agents who performed the usual checks (sign out of iCloud and sign back in, turn off Message forwarding and turn back on etc), I was finally transferred to a "Senior Advisor".
This senior advisor asked me to screen share my MacBook, iPad, and iPhone, to verify the problem. During the screen share, I showed him that text messages are only being received on the iPhone and not forwarded anywhere else. He performed several checks on my Macbook (like hold opt + cmd + P + R and power button, etc). I think these were the PRAM and SMC reset. Ultimately, neither helped.
On the iPad and iPhone, he asked me to sign out of iCloud, restart device several times and many other checks (some of which the customer care agents had already performed earlier). Nothing there either.
Finally, he said he would forward the case to "Apple Engineers" and would contact me back with a solution as soon as they have one available. This was on October 10th, and no news since then.
On 13th, he says he wants to do another call to "get more information requested by Apple Engineers" and asks me to let him know when I have the iPhone and all other "affected devices" ready. I send him an email right away saying "I'm available now", and I waited for his call all day, and yet, NOTHING. I send several follow up e-mails asking if he even plans to call up that day and NO RESPONSE. Not even a courtesy email saying that he can't make it today.
Apple - is this the expected behavior when your customers purchase a $1500 iPhone and these problems creep up within the very first week?