Frankly, the more I think about it, I think they should have a ‘proper’ male companion with the Thirteenth Doctor, for multiple reasons.
A lot of times in New Who, male companions have been ‘added on’ to the female one and that had often led to - sometimes humorous, frequently just hurtful - derision by the Doctor. Particularly if they cast a man of colour (and even more so if they cast a black man), it would be a chance to walk back on some of the uncomfortable elements of Mickey’s and Danny’s stories.
Plus, as @lyricwritesprose has pointed out repeatedly, a male companion to a female Doctorcan be a subversive choice that casts a new light on male strength and the Doctor/companion dynamic. It’s a new kind of story that deserves to be told. Not at the exclusion of a female companion, but certainly in parallel, it could enrich the show. We can have strong female relationships and a second interesting new take on the Doctor/companion dynamic.
And finally, as much I don’t care about the people who act like no boy could possibly look up to a female Doctor, the story of companion has always been special to me. There’s something captivating about it and that’s often been the case because these were stories about women. I’d love to see young boys get a chance to truly have this kind of connection to a modern Doctor Who companion and experience the kind of story that has meant so much to me in a similar way.
oh man if i was showrunner for doctor who i’d keep the casting of the 13th doctor and the companion under such tight secrecy and security like anyone who even thought about spilling the beans to the press would be shot at dawn but i’d let one set photo of this dude and this woman near the TARDIS leak and let everyone’s imaginations run wild on what he’ll be like as the Doctor and what she’d be like as companion and then in the first episode show 12 regenerating into the woman for the 13th Doctor and her meeting up with this new male companion and the remaining thirty minutes of the episode would be me staring down the barrel of the camera laughing maniacally
what if the next companion was a scientist who believes there’s no such thing as time travel and aliens and has lost all hope in this world and the doctor just comes along and shows him all the planets and stuff and completely changes his view of the world just an idea