Accent has little to do with the ability to communicate clearly.

In some cases it does. There are accents, even among English-as-a-first-language speakers that are almost unintelligible.

For example, many Americans struggle to understand the kind of English accent used by some recent immigrants from India -- immigrants who by and large speak perfect English.

Grammar might be perfect, but thick accents can be a tremendous impedance to communication.

In these cases it can be even worse since the speaker knows they're speaking correctly, but just can't make themselves understood, even in basic conversations. Accent training is the perfect and only solution.

Nothing against your general point but...

even among English-as-a-first-language speakers...

kind of English accent used by some recent immigrants from India

Those two statements don't work together. Almost nobody in India speaks English as a first language.

Well, I'll refine that statement a bit. There are, in fact, families in India who speak a lot of English in day-to-day situations. This works both as a status symbol as well as a tremendous advantage in the professional world. But I'll bet these are not the people whose accents you'd have trouble understanding. Kids from such backgrounds usually grow up watching a lot of American/British TV/movies and are usually able to operate fluently in an international (not just American) English speaking environment.

Correct. Let me add Ireland as a good example of that as well

I often get to translate what my Brisbane colleagues are saying to my Seattle colleagues. I'm from Europe and not a native English speaker. I suppose it makes me more indifferent to thick accents. However, Danish accents are too severe even for me.

It has little to do or it should have little to do with the ability to communicate clearly? Because I strongly suspect you mean the latter, not the former. There are plenty of examples of the former.

I mean the former. People communicate with each other just fine - with or without accents, with or without stutters, with or without lisping.

Accents are part of people's identity because of the nature of their mother tongue. The Italians have strong accent, as well as Russians and Indians. They are fine - they are not a deficiency.

Ban Ki Moon is a UN Secretary General - and boy, he has an accent. It works fine for him being a diplomat whose job is to talk and talk and talk.