We can generally understand each other but, as I discovered when I became good friends with a lovely lady from Portland, Oregon, when I lived in Madrid, it's sometimes a bit of a one-way street. I had no problem understanding everything she said, perhaps because I have always watched lots of American TV shows and movies. She, however, struggled much more with British vocabulary and was frequently baffled by things I said.
Precisely. Generally speaking, the world has way more exposure to American English than British English. I really don't see the point of teaching the British variety to learners who do not intend to live in Britain, or those for whom the major part of their communication is with native BrE speakers. And even then, there would be only very trivial intelligibility issues if those learners only knew AmE.
In a world where English is becoming more and more common as a second language (largely driven by Chinese learners, I think) and in which people are required to communicate not only with native-speakers from all around the world, but also with other non-native-speakers, the goal that many linguists have identified to be a future solution to the challenges faced here is the idea of English as a 'lingua franca' (ELF).
Regardless of the future of ELF, most teachers nowadays are faced with the challenge of attempting to teach some kind of global
standard form of English. I like to use the term 'International Standard English' (ISE). Teachers usually have a good intuition for which words are generally understood globally, and so will focus on these words and not on those words which are bound by dialect/sociolect/culture/region, etc.
To a large extent, this standardisation has already firmly taken hold in the world of academia (what you can call 'Academic English'), and to a lesser but still significant extent, in the world of business ('Business English').