Why is the Rani interested in Omega? Yep, the Doctor and Hedin, but she doesn't seem like the type to have heroes.
Also, in January 1983, it had been a bit over a year since the Three Doctors repeat reminded viewers of the character. Now it's a random name only people about 60 know.
It's an experiment. She's tinkering with the workings of the gods just like she would tinker with mere mortals. That family at the beginning certainly were specimens in a petri dish. And it is my prediction that in this case her tinkering is going to bite her on both of her asses.
As for why Omega? Because he's not the Master or Rassillon? Again?
Bring in someone from the newer era? Who? Create a new character integral to early Time Lord lore? Last time someone did that fandom threw a connection fit for daring to tamper with what they already knew and loved.
Create a brand new villain on the spot, or even just for the season? Where is the investment? Where's the conversation? One and done seasonal Big Bads tend to elicit a big shrug from me.
The canvas of Doctor Who is so big that it seems detrimental and self-defeating to simply decide that certain parts of it are no longer relevant just because newer viewers weren't familiar with it yet. There was a time when newer viewers weren't familiar with Daleks, Cybermen, the Master, Rassillon, Gallifrey and Timelord society and history in general. I know I wasn't. My first episode was
Day of the Doctor and I started that journey with very little knowledge of any of these specifics, and I never felt lost or confused.
My journey through new and classic Who was a simultaneous one. In fact, I watched
Tomb of the Cyberman and
Rise of the Cybermen on the same night, before ever having seen
The Tenth Planet or any other Cybermen story. Didn't feel lost in the slightest.
Sorry, but the attitude of not tapping the show's own history mystifies me.