Fam flights still exist and the fact that 9/11 stopped them is a myth however some companies will be more flexible than others! It seems the onus seems to be on the controller to arrange it rather than NATS etc teaming up with operators and offering fam flights to controllers and assistants - which of course would be easier! The fact that the trip neeeds to be done on a day off is another factor that might turn off some who may have hectic lives outside work and may not wish or can devote the time.
My current company and my previous have been more than willing to have ATCOs and ATSAs on the jumpseat on a fam flight (post 9/11) and the ops manual from my current company clearly states that ATC staff are allowed jumpseat access on pre-arranged fam flights. Normally a couple of e-mails between ATC and the operator concerned is all that is required and any bits of security paperwork getting filled in by the operator.