That's not 'more relaxed' pronunciation, it's a set of different accents (not a phenomenon unique to English). People don't arbitrarily mix and match between them, and any particular accent preserves enough vowel distinctions to largely keep different words distinct. That's different from a learner using the wrong vowels randomly.

The underlying linguistic issue here is that when we're young our brain trains itself to classify speech sounds into categories based on the speech we hear around us -- so sound differences that matter in our native language(s) go in different buckets, but differences that don't matter in that language are ignored. That makes it harder to learn a different language later where the bucketing is different because our brains naturally ignore sound changes that should be significant, and need retraining.