I haven't listened to The Apocalypse Element in a bit, so I've kinda forgotten large chunks of it. But based on what other people have said, I was expecting the Doctor to be dismissive of Romana on my relisten.
And, by my read, this doesn't happen. Like, don't get me wrong, from Romana's perspective this was rough treatment. But I've been getting the vibe that the Doctor doesn't seem to care about Romana, and I very much disagree with that. Firstly, as soon as he knows she is in danger, he is bringing that up constantly until he finds her, and while he is somewhat collected when talking to Vansell and the President over it, I see a lot of pain and rage behind every line he says in that scene.
And yeah, once Romana is back, his actions aren't the most caring, but they did not have time for that. He's trying to keep as many people alive as possible in the story that is probably in top five for body count in the entire franchise. And yeah. Does he also express a lot of concern for Evelyn? Yes. It's an awful situation, but Romana - battered and broken as she is - is a Time Lord. Time Lords are good at not dying. But in this story, feces is hitting the fan, and the Doctor is trying to keep his friends and the universe alive.
As for him just leaving at the ending, there's actually a really good reason for this. He's really not supposed to be on Gallifrey. Romana returned from E-Space and became president during the Seventh Doctor era - this is all in the Doctor's future. He might have had some idea that Romana came back from E-Space, but he had no idea she was president. That's all in his future.
This isn't just my usual canon-welding wankery either - the Doctor is shocked when he learns that Romana was president, and when Romana sees him, she notes that he is in "the wrong body" (since she was expecting the Seventh Doctor), and the Doctor responds by saying he is in "the wrong time" (Seventh-Doctor era Gallifrey). While the background from that was from the Virgin New Adventures, tae is building a lot on the VNAs - in as much as that's where the idea of Romana being president comes from - so that combined with how those lines are delivered makes me confident that I'm reading into something the author inteneded.
So the Doctor is in Gallifrey's future, and that's something that's really not supposed to happen. This is the sort of thing that's a paradox in the making, and this is when Gallifrey is still trying to just keep its hands clean of that sort of thing. He can't stay with Romana and Romana can't leave with him because there is a 200ish year gap between their histories and ignoring that is a great way to bring the Gallifreyan legal system down on their heads.
Does this suck? Yes. But I don't see a way for the Doctor and Romana to have stayed together that didn't give Vansell an excuse to go after them (especially since other sources state that Vansell was basically behind the Trial of a Time Lord stuff - and I will grant that that is my usual canon-welding wankery, but I think the point still stands without that detail).
If you want to criticize the Doctor for trying to sneak off at the end and not trying to have a proper goodbye, then yeah. I'm there with you. That's in character for him, but it's not a great thing for him to do.
But if you want to criticize the Doctor's other actions during The Apocalypse Element, while that is of course totally valid, I do not think I agree with you.