Agreed. Although, America has what's considered the "non-accent." It's the mass-media accent you would find on American television. I would venture to say that a significant segment of our population speaks with this accent.
It's downright embarrassing for me when I hear Americans with southern accents. I also cringe when I hear certain British accents which torture their vowels. For instance, when pronouncing the word "no", they say, "nah-ooo" with two syllables. It's aurally painful!
You're right about that too. The southern drawl has a habit of inserting extra vowels and (ay-and) syllables.
Personally, I speak with a mix of hard & soft t's. Sometimes it's "whaddever", while others it's "whatever" with a hard "t". It depends on the situation, whether it be casual, professional, serious, jovial, etc.
I've heard Brits completely omit the "t" in some words. It is more comical than anything. Instead of "not" with a hard "t", it's "nah" with a glottal stop and short breath after it.
How about those BBC newsreaders who append an "r" after words ending with vowels? China becomes "Chiner" -
Of course, to truly understand why we round off consonants, you'd have to consult our dead ancestors for leaving us such an undisciplined inheritance.