Most foreigners are trying to speak the best English they can. They want to be grammatically and linguistically correct. They try to stay away from slang, from certain colloquialisms, such as "Innit", which is a not just very much a London sound, but a very "native" sound.
Most of us will be unable to shift or let go of our accents, I do sound Norwegian, or at least Scandinavian when I speak. You can easily distinguish a Polish from a French person from their accents, in the same way as you can distinguish a foreigner from a native English speaker.
Wanting to communicate correctly and be understood by native English speakers and foreigners alike is not snobbery. It is just a realization that our own foreign accents coupled with a mix of regional variations will make us sound ridiculous, and stand out in ways we dont want to stand out.
Have you noticed the way people correct grammar on this site? And pick on posters' use of English or their literacy skills?
This happens real life, too, you know.
I have lost count of how many people will actually stop me mid sentence to point out a pronunciation error, such as "Quint, you know you dont pronounce the L in salmon, you say sammon" etc. Or, "Quint, in London we say baarth not beth, in case you had not noticed". Etc Or just the word pronounced correctly, slowly, repeatedly.
I am shocked that so many native English speakers get their knickers in a twist and see it as "snobbery" when foreigners want to speak a consistent clear English, rather than pick and mix various accents happily. We just dont want to be judged, and laughed at.