Oh no, I’ll definitely agree that Yaz and 13 isn’t done great at all (at the very least from 13’s side), to be honest, I’m not the biggest fan of 10/Rose or 13/Yaz in terms of shipping but they were definitely both intended to be read that way
Speaking of 13 and Yaz, dropping one of my favorite Doctor Who analysis videos here
I have 0 clue at all where this ship came from (I think maybe some Doctor Who Roleplay serve) but I think it’s very funny. Definitely not something I actually ship though
I think Chibnall was between a rock and a hard place here.
He’d seen the speculation and the theories about Thasmin and it was all new to him, he hadn’t ever considered it.
So he was damned if he did - he’d be accused of pulling it out of nowhere and queerbating - and damned if he didn’t - he’d be accused of probably a little bit of queerbating but also have angry Thasmin shippers attack him for doing nothing.
Basically it would have been better with a plan from the start, but he didn’t really have a plan for any of the companions, which is why they all just said “Ok see ya later” at the end instead of having satisfying reasons to leave. But that’s another complaint lol
Well, if we’re going to go all shippy…
MASTER: Goodbye, Miss Grant. And goodbye, Doctor. I sincerely hope we
meet again very soon.
(The Doctor nearly shakes the Master’s hand, but turns the gesture into
a wave.)
DOCTOR: Goodbye.
(The Master gets back on his rowing machine, laughing.)[Governor’s office]
JO: Doctor?
DOCTOR: Mmm?
JO: You felt sorry for him, didn’t you. You wanted to come down here
and see that was all right.
DOCTOR: Well, he used to be a friend of mine once. A very good friend.
In fact, you might almost say we were at school together.
JO: How long’s he going to be here?
DOCTOR: Forever, I should think.
I don’t think Yaz has to be more “special” than other companions for the doctor to fall in love with her. I do prefer it being unrequited though, partially because I just like stories like that.
I prefer ambiguity in cannon when it comes to the doctor’s “love interests”, but I ship the doctor with a lot of different characters. Shipping ≠ wanting it to be cannon
DOCTOR:[to Peri] I can’t think why you’d want to stay with me. If you do want to stay with me, that is, I might even let you borrow my body again from time to time, if you asked nicely…
Given this is now a topic, what’s everyone’s number 1 ship for each doctor?
Four: Sarah Jane or Romana II
Six: Peri
Nine: Rose
Twelve: Clara
Thirteen: Six
I don’t ship the other Doctors with anyone.
2 - Jamie
3 - Delgado!Master
4 - Romana
9 - Rose/Jack (polycule)
10 - River
12 - Clara/Missy/River
I’m sure there’s more, but that’s it for me off the top of my head
1 - Cameca
2 - Jamie
3 - The Master
6 - The Doctor
4 - Erato
Personally, I think the only good pairing for the Doctor has always been, and will always be, The Master/Missy. Twissy especially. Outside of that, I don’t think there’s a good pair for the Doctor. In terms of companions however, I’m a firm believer in Tyssa.
I’ve never been a ‘shipper’ but I will say that I definitely picked up on 13/Yas vibes as early as Spyfall so it didn’t necessarily come out of nowhere for me, even if it wasn’t being planned by the makers at that point.
A strange paradox there, but I can basically see why people started shipping them, given that I thought that was the intention.
I’ve said before, I think Yas gets a pretty raw deal from fandom because I think she’s one of the most well drawn characters for a while. And because I think that, and because she definitely feels more real to me than some of her predecessors, I can see what 13 saw in her.
But again, I don’t think this makes me a shipper, I just watch and experience drama and have views and thoughts on it. I don’t necessarily want two characters to get together, I just watch their relationship develop and either like it or don’t.
@shauny is right as well, Chibnall was going to piss a vast swathe of people off whatever he did with 13 and Yas when he discovered they were being shipped. But then, that’s true of whatever he did during his tenure in my opinion, not just those two characters!
Honestly it’s hard to know which ones to single out as my favourites. There’s a lot of ships I like to explore. I guess the ones on my mind the most right now are 8 x Charley and 3 x Joe
This does not include the Doctor but I’d love to ship Rory and Jeff (The Eleventh Hour)! 
First Doctor: The TARDIS
Second Doctor: The TARDIS
Third Doctor: The TARDIS
Fourth Doctor: The TARDIS
Fifth Doctor: The TARDIS
Sixth Doctor: The TARDIS
Seventh Doctor: The TARDIS
Eighth Doctor: The TARDIS
Ninth Doctor: The TARDIS
Tenth Doctor: The TARDIS
Eleventh Doctor: The TARDIS
Twelfth Doctor: The TARDIS
Thirteenth Doctor: The TARDIS
Fourteenth Doctor: The TARDIS
Fifteenth Doctor: The TARDIS
I think that just about covers my stance on the matter.
(Also want to clarify that I do in fact mean this in both senses)
I am the complete opposite. I don’t see Yaz/Thirteen at all and I think it was very rushed and should have remained unrequited if they were going to do it at all, but I think the few moments we do get of Nyssa and Tegan together could be indicative of something more if you’re already used to combing through shows for lesbian subtext. It’s fully possible my opinion on Yaz/Thirteen would change with a rewatch, and I’m definitely not saying Nyssa/Tegan is anywhere close to being canon, but one I have no interest in and the other I can at least see.
You’re probably joking @lwebb, but I have a serious question for people who ship the Doctor/TARDIS. Do you ship them in an affectionate “old girl whose been with him through thick and thin” way (so no more romantic than a person with a strong attachment to a car or a boat they call ‘she’, and no sexual activities are involved) or do you imagine the Doctor kissing her and fidding with her gadgets and gizmos? I hear a lot of people say they like this ship, but I can’t tell which field they’re actually playing on and if they’re being serious.
Personally, I view shipping as basically saying “I find their dynamic interesting and watch to explore the potential sexual and/or romantic aspects of it in various ways”, which means I don’t really ship the Doctor with many companions if at all. I tend to find queerplatonic relations a lot more compelling and interesting for them. I’m happy to read fanfiction and meta analysis, especially for Doctor/Master, Twelve/Clara, and Eight/Charley, but I don’t think I really properly ship them.
To answer @CommanderBayban’s question: it’s often a mix of both. Yes, it’s a bit of a joke about someone being in love with their vessel, but it’s also very much about the other stuff. The TARDIS is very heavily implied to be sentient and even sapient in some way, likely telepathic, so it’s not much of a leap to assume she and the Doctor have a way of communicating. Now, if you want to know more about the physical aspects of such a relationship, I suggest you look into objectum.
