They've been weirdly stingy about using Davros
The new who writers I don't think and I know this is going to sound pretentious, but I don't think they have the patience to write a villain like Davros.
I'm not saying Davros is high art, or even more complex than the Daleks or Cybermen, but it does take a bit more patience to make the actual villains like the Master, Davros, the Rani, Omega etc interesting.
The Daleks, Cybermen, Sontarans, are all so colourful and charismatic you can fall back on their presence more. You still have to do something new with them obviously, but it feels a lot easier because you know as soon as they are on screen people will be happy.
The Master however, well as good as the actor is, he is still just a guy. Davros meanwhile actually falls more into this as though he looks horrific, he is somewhat harmless physically and so in both cases you really have to take your time to build them up into being legit threats.
Given their crash bang wallop style, and their limited time span, they are stingy about using all of the more humanoid villains compared to the monsters.
The Master was in just five episodes of the Tennant era. Moffat didn't bring him back at all in Matt Smith's time, despite Simm saying he really wanted to come back to Moff at the wrap party for End of Time. (Contrary to popular belief Simm doesn't hate the show. There's quite a sweet story of him at a convention telling a little boy whose favourite villain was the Simm Master that he's not dead and planning his comeback.)
Still Moffat didn't use this popular actor (I might add Matt Smith also wanted the Master back) throughout the entire era, and only brought the Master back as Missy when he saw an opportunity to squash the he is sexist rep by gender bending him.
You and I both know that Missy isn't the Master. She's not even a rebooted version like Simm. She just isn't the character. She is River Song 4.0. mixed in with desperate political pandering. Moffat hated the Master and said he just did his own thing, which is what makes these "Missy channelled Delgado" people look even more stupid.
With this in mind I don't count Missy as appearances by the Master. The next appearance of the Master therefore is Simm in the Capaldi two parter. Taking all of Simm and the Dhawan Masters appearances together, the Master has appeared in just 12 episodes of New Who. (7 for Simm, 5 for Dhawan.)
That's less than almost all the monsters.
Cybermen 25 episodes, 26 if you include Cyberwoman from Torchwood
Daleks 31 episodes
Sontarans 15 episodes.
Silurians 13 episodes (including the upcoming christmas episode.)
Weeping Angels 9 episodes, 10 if you include Class.
Judoon, 10 including Sarah Jane Adventures.
Ood, 7 episodes
So yeah the f*cking Silurians have been used more than the Master, how insane is that? Even the Angels Judoon and Ood aren't that far behind him, and were leading until the Jodie era.
Meanwhile out of the others, Davros is only in 5, Rassilon in 3 (all of which he was pushed to the background.) They have point blank refused to use the Rani, the Valeyard, Omega, the Monk, the War Chief etc. You could say well they were all only minor villains, but again they've brought back minor, one off monsters, like the Zygons, the Macra, Sutekh etc.
Also look at their attempts to create humanoid villains. Well the better thing to say would be what attempts? Madame Kovarian and that's it! They just don't like that style of villain.
