I was wondering about the same thing when, after years of learning English from tapes, BBC news, comedies, etc., i.e. mostly listening to RP, I started travelling around the UK and noticed, to my horror, that almost no one speaks with such accent. What's more, initially I was often told things like "wow, your accent sounds very posh/upper-class" or "how come you speak RP?"
I used to explain that foreigners often learn from tapes and TV, and so on. Then I realised how many different accents exist within the UK (not to mention the English-speaking world) and that speaking RP, though probably does make you sound a bit posh, is not really that important.
I think that the most important thing is to be understood by the people you will talk to; there was a discussion on this forum some time ago and one of our Moderators said something along the lines of "I couldn't care less about the accent as long as your pronunciation is correct". Need I say more?
It's just like with any other language - for example, you are from Chile and I have always learnt Spanish Spanish, but I have no doubt we will have no problem understanding each other.
And let me finish with an anecdote - because of my job I get to meet people from various parts of the UK and the English-speaking world. Most of them will detect that I'm not local, as the city where I live has a distinctive accent which I don't try to imitate. Therefore some try to make a guess - and in 90% of cases it's... "You're from South Africa, aren't you?"
Student or Learner