I would like to point out the reason why H is called aitch is a historical one arising from French, which was spoken in britain for several hundred years after the whole William the conqueror thing.

In French, most h's are silent (ie, soft sounding letter without an audible Huh sound). There are exceptions (le haricot, le hamburger), but on the whole most of those h's are soft, and the letter itself is called "ache" (pron. "ush"). Allegedly, nearly a third of words in English have French origins, so a lot of the words we now pronounce with an aspirated "huh" probably started with silent h's. But nobody has gotten around to adjusting the name of the letter.

That's why you still come across people who insist on saying an hotel and an history.
I say it as aitch, but I would be confused if someone said an hotel or an history, as if the h was never there at all. To me it's always a 'soft' sound or letter, you breathe the h part and the 'harder' sound comes from the next letter. So in hotel, you breathe the hhh sound and the next sound comes from the o. I can't think of any word where the h letter is actually pronounced like huh, it's always just kind of breathed.

If people were not going to say anything at all for h we may as well take it out of the alphabet.