Do you think accents are an important part of learning a language?

[A_Son_of_God]

So, I was considering an event where a person I had to deal with in a business environment, although they technically were speaking English, were so hard to understand, I didn't agree that it was in good corporate image to have them representing the face of communications for their business. They were a bulwark to understanding, due to their lack of pronunciation and inability to get their message across in the English language.

I got around to looking online at people's opinions on this issue, and found a couple of sources where this has been considered in some context, and a specific body deems it unimportant to have to learn an accent-specific language. The problem though is that they seemed to be coming from the context of English native speakers, teaching people English.

My angle is that I have friends from all over the world, and that for anyone to improve in their language, it isn't the language itself, but their pronunciation - or lack of it - that leads to errors. The two sides are that some deem it racist to find a funny side to an accent, whereas the accent itself is a critical part of understanding on the part of the hearer.

If I went to a country and wanted to learn a language, surely I'd want to consider the pronunciation, so that the listener would understand me. Not so that I could technically get away with saying I passed their language, when in fact, nobody can understand me fluently.

What about you? What are your thoughts on it?