marduk
quelling chaos since 2352BC
If I remember right, the chameleon circuit is broken because his Tardis is so old. The Master has a newer model where it works.No reason why not.
The masters Tardis can also have any external appearance it likes.
Exterior
During his rivalry with the Doctor, the Master changed his TARDIS into several different forms, including: an Adjudication flyer, an out-of-date space locker, a horsebox, a white cube, a spaceship, a black Rolls-Royce limousine with darkened windows, a bulkhead door aboard the HMS Redoubt, the Stone of Sacrifice in the cavern of the church at Devil's End, a computer bank, a filing cabinet, a control panel, a wardrobe, a grandfather clock, a tank,a red pillar box, the Melkur, a police box, a laurel bush, a Doric column, a marble fireplace, Speedbird Concorde 192, an iron maiden,a three-sided column, a wooden beach hut, a statue of Queen Victoria, a red telephone box, a transport crate , a palm tree, and a white pillar.
My question is would fans be happy to see the Doctors Tardis change from a blue Police box and start appearing as other things ?
Personally i think such a radical change would be a bad thing, like knocking down a lovely heritage building to build a concrete and glass tower.
I see a poll in the Mirror still has a large No vote for the change 63/37.
BBC sparks furious backlash after Jodie Whittaker female Doctor Who announcement
Personally i think the Doctors Tardis should stay a Blue Police box even though there is no reason why not it could change
And for the same reason i would prefer the Doctor remain a man. But i'm old and have been watching the show since the 60's.
What I'd really rather see the Beeb do is more shows along the adventure in space and time show. Cast excellent look alike's and do new stories about older regenerations.
I could envision a prequel (I don't think they ever say Hartnell was explicitly the first regeneration) where he has a Tardis with one that works.
If it were me, I'd probably program it to look like Magnum PIs red Ferrari.