All fair points, except you have a multitude of different races. Which are dramatically more diverse than different ethnicities of Humans. That is why it makes no sense for Goblins, Drow, Hobgoblins, Tieflings, etc. to all sound the same. Drow exist miles beneath the surface, in what might as well be the other side of the planet. Moreover, Lae'zel did not grow up on the material plane, based on her available dialogue. Your arguments are fantastic for why they all would speak the same Language (Common) but not why they would all share the same accent.
We have a multitude of examples of varied accents even among similar locales in D&D, namely BG 1 and BG 2. It makes no sense why that also isn't the same for BG 3.
I would argue they will have different accents when speaking in their native non-Common languages and similar Common accent, for Common-speaking people use it as lingua franca and likely learn it from each other - so I'd expect Common to be a sort of a more or less unified mix of various influences in terms of the accent. Just as in real life people who learn a second language in early childhood commonly have an accent from where/whom they've learned that language, not from their first language.
And in BG3 they DO have different accents and most certainly don't sound the same. I can tell even despite not being British. Goblins in particular, whom you've described as sounding the same as everyone else, have distinct Cockney accent. Someone said there's a character with a Welsh accent. They are different, but realistically different, not exaggeratedly different. I think it's very appropriate for the circumstances, as swampslug described it. Also in real life, different places have different language variance. Some have a plethora of dialects and some are quite unified with differences between regions and social circles being minute.