Your list is a bit rough. I could see why you labeled these champs as control mages, but primarily, many of them are not.
Normally, when I think of control mages, I think of a mage who has control over an area in the battlefield. Normally, they involve manipulating terrains or covering a wide area of aoe damage or cc without them having to jump in close range
These abilities are normally the essential part of their kit, so they are normally integrated their regular abilities.
has her wall and ult
has his ultimate with its aoe damage
has her grounding effect
has his mini turrets and ult
has her root and ult
some what arguable, has her ult and root
has her ball
has the AOE damage on minion wave and ult
her scattered balls
not really
has his stunning field and ult
has his bombs and ult
has her plants and ult
You are missing potentially
who has his soldiers and ult, and
who has her rock field and ult.
Out of any mages there whose kit revolve mainly around taking advantage of the battle field, I would say it
. They make it hard for anyone to engage due to the field they set up, and the wide area they cover, without having to sacrifice much of their range, though the rework on Azir hurt him from fulfilling this role as much now.