"Daft modern nonsense"?
No, it is not. Do you like the same characters as I do in various TV shows or movies? There are likely some for which we're on polar opposites, just in the reverse (I like them; you loathe them). I don't march into the Voyager forum and declare that it's "daft modern nonsense" to hate Seven of Nine and Tom Paris (two characters I happen to like, while many other fans don't). Criticize the character, not the fans.
How is Romana in any way similar to Clara? Romana is Gallifreyan, an Academy graduate, and grew as a person from the naive, arrogant just-graduated-and-I'm-so-smart airhead in "The Ribos Operation" to the no longer naive, less arrogant, got-some-life-lessons Time Lady in "Warriors' Gate" who was ready to take on E-Space with her own TARDIS (after building it, of course), companion (K-9), and a mission in mind (freeing the rest of the Tharils from slavery).
Clara is not Gallifreyan (despite all her wishful thinking and bizarre statements of "I'm the Doctor"). She was always a motormouth with an attitude. And the only way she gets to scamper around in her own TARDIS is because she's using a loophole that keeps her from dying, as she was supposed to do. At this point I have to ask: Was there some notion of spinning Clara off into her own TV series?
The thing is, this sort of stuff is jarring to many of the Classic Who fans. The first time there was ever any slightest
hint of anything more than a platonic relationship was in "City of Death" - and all the Doctor and Romana did was hold hands as they ran through the streets of Paris. You could interpret that as the Doctor not wanting Romana to fall behind, rather than any type of relationship that wasn't the elder Time Lord mentoring the younger, less experienced Time Lady.
After that... well, the Fifth Doctor definitely noticed Tegan's cleavage in "Enlightenment" (who wouldn't?), and the Eighth Doctor kissed Grace in the 1996 movie (since they didn't actually go anywhere in the TARDIS, could she really be said to be a companion?).
In other words, Clara = Mary Sue. She's sooo much more important than the Doctor, because without her, he wouldn't exist.

. Like no other companion has
ever done anything to help him avoid getting killed or saved anything.
"City of Death" didn't require a flow chart to figure out what was going on. About the most complicated stuff that might have required one was the Dalek/U.N.I.T. story arc in the Third Doctor's era.
Once that whole mess with Amy and Rory and Riversong got going, I just gave up. It shouldn't require a flow chart and repeated viewings to figure out WTF is going on. To me it just looked like a case of "Oh, damn, we've written ourselves into a corner
again, so let's pull some timey-wimey thing out of thin air and pretend we meant for it to happen all along."
That's the impression I got with Clara, as well - that it was just made up as they went along. Write yourself into a corner? Actress keeps changing her mind about leaving? Pull out some outrageous new Mary Sue thing!
I didn't get to see many Zoe stories, but the thing with her was although she was really smart - and
knew she was really smart - she wasn't arrogant or unlikable about it.
Liz Shaw regarded the Doctor as an interruption in her already-planned life. She'd had a job lined up when she was abruptly pulled away from it and assigned to U.N.I.T. and to be the Doctor's assistant, when she was already a doctor in her own right.
If you watch from "Ribos Operation" through "Warrior's Gate" you'll notice that Romana grows as a person from a naive damsel (think Rodan in "The Invasion of Time" when she and Leela escaped from the city to join the Gallifreyans in the wilderness) to a very capable young Time Lady who prefers to strike out on her own, rather than return to the stifling society of Gallifrey.
Being able to talk fast is not a sign of intelligence. It's just a sign of being a motormouth. Considering that I found Rose's accent hard to follow at times (she seemed to talk through a mouthful of marbles on occasion), at least I never had to use the closed-captioning for her as I had to for Clara.