[lambdadmitry]

Adding to what Xophmeister said, IPA isn't just a notation, it's also a tool of thought. First, to efficiently quantize the stream of sound you need mental "buckets" to put the sounds to, and IPA provides your those buckets. Second, it may seem as if we hear "objectively", but in fact what you hear is very much affected by your language upbringing; for example, a ton of Americans can't really differentiate "pin" and "pen" even if the words are pronounced as in Standard American — they don't have a concept of the sound needed. IPA gives you those concepts.

[schoen]

That's a terrific way of putting it! Maybe we can say that IPA reminds of the challenges that are still out there for us in terms of distinctions that we overlook and sounds that we can't produce.

For example, I haven't learned to distinguish /pʰ/ and /p/ or /bʰ/ and /b/, as Hindi does, but thanks to IPA, I know that that issue exists and maybe I can learn it some day. Also, I haven't learned to say the consonant at the beginning of a Chinese friend's name (I think it's [ʈ͡ʂʰ]), and IPA helps remind me that [ts] and [tʃ] are just approximations to it.

[lambdadmitry]

Exactly! Moreover, even if I didn't learn the exact sound you are talking about, I can sort-of approximate it in my head. To be able to "transmit" sound in text is a proper super-power I would say, not too far from what Arrival pictured :)