Why the Characters of Mass Effect Andromeda are well written.

I disagree with the OP, and I think you've touched on what about the game so irked me.

All of the characters in Andromeda come from a very similar place and undergo a very similar arc and that is the problem with them in my opinion. There is little variety within the crew between their motivations and eventual place in the crew. Furthermore many of them are characterized similarly to each other.

Let's start of with some of the character's backgrounds.

Vetra is a turian smuggler raised outside of the normal society of turians and seemingly isn't part of the rigid turian way of life existing largely on its periphery.
Peebee is an asari, who doesn't particularly like other asari, and exists independently of the asari ark and the Initiative as a whole.
Drack is a krogan, who goes off on his own to fight his own war against the kKett.
Javik is an agent of the Anagara military...but operates seemingly independently of their command structures.

Can you detect a trend? All of the companions start off as outsiders and try to grow closer together as a part of the Nexus crew. This is also seen somewhat with the others on board the Tempest as well. Lexi seemingly has trouble fitting in with social situations, SAM wants to form a weird symbiosis to further understand humanity, etc...

This isn't inherently a problem, and a unifying theme among the crew isn't a bad thing really. It can help tie together the themes most present in the narrative. ME2 in stark contrast had none of this and each character's themes and narrative purpose are almost wholly independent of each other.

However, I don't think this worked in Andromeda very well for a few reasons. First and foremost, there's very little sense that the characters have matured over the course of the game. There are some scenes that hint at a growing sense of maturity, but they are often restricted wholly to the end of the loyalty mission and never brought back up again. The character slides right back into their pre-LM manner as soon as the mission is out of your journal.

For example, Peebee ends her LM with a confession to the whole crew and is surprised at their acceptance of her. Yet this is not reflected in a substantial way. She still stays in the escape pod (because what is subtlety). Drack learns a valuable lesson about the limits of his ability to protect his granddaughter and the role that he sees himself playing for the krogan settlement, yet this is also not reflected in any change.

Now on top of this throw the writing of the characters themselves. At times they can pass muster from the original trilogy and I won't argue that the OT was flawless in regards to well done character writing.

But there were no moments such as Liam talking about shooting people in the face. Now some instances of this dialogue are acceptable. Cora's juvenile adolation of the asari is to set up her realization later on, and the infamous Suvi/Ryder flirting has its defenders as awkward flirting. But these reasons cannot encompass all of the writing mishaps and when piled on to characters that are often very similar in arc and origin, to say nothing of the repetitive nature of the writing, it doesn't stack up well in comparison to the highs of the original trilogy.

There's no Mordins or Legions to be found in Andromeda's crew.