Part of the problem with the phonetic alphabet, though, is that it only allows for one accent. Dictionaries will sometimes give variations, granted, but if you don't know how to pronounce the word (hence why you're looking it up in the first place!), you might end up choosing the wrong one for your own accent.
I remember talking to a customer assistant for an insurance company a while ago and he gave me his name for reference, as it was a slightly complex matter. His surname was Cornforth, which he pronounced in his broad Lancashire accent as (what sounded to me like) 'Carnforth'. I repeated his name back to him exactly as he'd said it, but he knew that I'd heard it wrongly as, in my Midlands accent, it shouldn't sound the same as in a Lancs accent.
Obviously, it's a very well-known word, but taking 'bath' as an example, supposing you lived in Kent, with a local accent, and didn't know how to pronounce it, you could end up choosing the same pronunciation for just that single word as somebody with a Yorkshire accent would use and then you'd just sound quite odd! Even with a common word like that, it's not simply a case of choosing between two options and either rhyming it with 'math(s)' or 'hearth' - many people in the West Country and South Wales would pronounce it somewhere between the two (with a drawn-out 'a' rather than 'ar' sound); and that's not even getting into the common Estuary pronunciation of 'th' as 'f'!