There's got to be some sort of obligation to constantly use the Daleks, as we have yet to truly go a year without the Daleks period. Even 2016 had Daleks in Pearl Mackie's introduction video, and one could argue we got a "new" Dalek production with the Power of the Daleks animated reconstruction.
But getting back to what I was saying, not a single Dalek-free year since the show's return, with episodes like Waters of Mars and The Wedding of River Song providing meaningless Dalek cameos which served no purpose at all except being the only Dalek appearances of the year. Indeed, TWORS especially stands out, since prior to season 6 Moffat was promising no Daleks for the year in interviews, then after the episode aired when asked for an explanation on the matter his response was "I thought there wouldn't be any Daleks this year." Sounds to me like he was arm-twisted into showing the Daleks against his wishes.
Indeed, I've noticed, season 6 aside, Moffat almost always has his Dalek episodes very early in the season, the longest wait aside from season 6 was season 5 where they were in the third episode. From season 7 onwards they've always been in either the first or second episode (or both in season 9). The earliest RTD ever had the Daleks in a season was season 3, the fourth episode. Kind of seems to me like Moffat is trying to get the (obligatory) Dalek episode done and out of the way at his earliest convenience so he can get someone off his back. Curiously, RTD did confirm in The Writer's Tale that the BBC was always trying to pressure him into using the Daleks in a premiere, which Moffat has done twice.
Maybe it isn't a contractual obligation, but there is definitely some sort of obligation to use the Daleks every year, at this point it's damn near difficult to pretend otherwise.