the thing (well, one thing) about moffat is that he keeps creating these mysterious characters who are feisty and special and different and they cross timelines and they live in paradoxes and broken worlds and they are interesting and cool.
but they are not relatable.
whereas rose was us, working customer service with no immediate prospects.
martha was us, going to school and dealing with family crap.
donna was us, nothing special until she went on an adventure and learned how special she’d been all along.
moffat writes the companion he thinks we all want to be. rtd wrote the companion we all could be.
I dunno, I was able to relate to and identify with Rory pretty deeply, and Amy to a somewhat lesser degree.
Same with Craig even.
Not so much River, but then I’m not sure we the audience are meant to be able to relate to her as much.
Just because they aren’t relatable to you doesn’t mean they aren’t relatable at all.
And while I’m at it:
Rose - became special vortex-spewing Bad Wolf Rose and crossed the void how many times to get back to the Doctor? Let’s not forget how she created a paradox by trying to save her father’s life.
Martha - became special world-saving Martha by walking the Earth for a year, a year in which is now a different timeline.
Donna - became special DoctorDonna by helping to create the Metacrisis Doctor and subsequently getting his essence stuck in her head. She also spent time in an alternate timeline in a world without the Doctor, a world which was broken.
Words bolded for your convenience, because the ‘negative’ tropes the OP associated with Moffat can also be applied to RTD’s companions.
Amy - was one of us, a girl with big dreams stuck in a small town with seemingly no way out.
Rory - was one of us, just wanted a life surrounded by people he loved and a job he enjoyed.
Craig - was one of us, pining after the girl of his dreams and too shy/insecure/scared to admit his feelings.
I’m sure others could come up with better descriptions of Moffat-era companions to show how they are relatable, and RTD companions to show how special snowflake they were, but there you go.
Amy - a girl whose world was broken even though she barely knew it, who found a mad man with a box who showed her the universe and in the end, she put her life back together. she recovered what she had lost, by her own initiative, with help from the Doctor, but ultimately her mind rewrote the entire universe, brought her parents back, brought the Doctor back.
Amy’s S5 arc can be read as analogous to someone with the mental health disorder who has the chance to actually fix themselves. which is about as realistic as, well, the TARDIS. but that’s why we watch the show. because we see things that we’ll never see in real life. Amy rebuilds the universe in a way that makes her whole again. I think a lot of people can relate to that desire, even if the experience is beyond the realm of possibility.
I’m too lazy to come up with the others, but I see red when people discredit Amy Pond as a character and some one to relate to and be inspired by, when they clearly missed the point and depth of her S5 arc.
Yes the treatment of her character since then has been extremely questionable, and probably Moffat’s biggest screwup (though as patchy and muted as her characterization has been at times, she does have a personality loosely consistent with her state at the end of S5 so stop saying that - there’s a difference between bad writing and a bad character)
She’s a girl whose life became a story, and in the end she wrote her own ending.
She’s plenty inspiring.