Are you saying people who don't pronounce their aches should use "a" and not "an"? Because that would sound weird trying to pronouce two vowels like that.
We have two main ways of saying words like "hotel". I (with a rather non-descript vaguely southern accent) pronounce the H in hotel, and so say "a hotel". Many people from London and the south east (especially Essex and the parts of the home counties that has a large influx of North Londoners) will generally drop their leading "H" and say "an 'otel".
There is a third accent which is a minority, the rather extreme upper class accent where they also drop a lot of their leading Hs, and therefore use "an". That's not "posh cockney", that's just "posh", a lot of them have always spoken like that. Even among the posh I'd rank that accent as relatively rare these days.
Id does all lead to the occasional argument among slightly dull people about whether you should write "an hotel" or "a hotel".
US English calls herbs “erbs”, regardless of whether or not one is an aitch-speaker or not. Whereas “historic” is largely pronounced with the aitch, but you will find hypercorrectors who say “an historic” without dropping the aitch.
But some American dialects (midwest?) have dropped the use of "the" with a long 'e' before words beginning with a vowel.(ie: thee apple)
It sounds bizarre to me to use the short 'e'.
Some Americans whom I've met (I think Midwest ones, but not sure), also pronounce the word "often" as oft-en (but without any pause). I don't know how the British pronounce it. In India (having learnt somewhat British English), we pronounce it as "ofen", sort of rhyming with oxen.
And of course there is the famous "shedule" vs "skedule" pronunciation for schedule.
