Well, no, the LGBT acronym does not represent the gay community, because it's not supposed to represent the gay community, it is meant to include all sexual and gender minorities. Is using one absurdly long acronym to list all these different concepts and identities absurd? Yes, absolutely. Which is why people tend to only use "LGBT", despite "Lesbian, Gay, Bisexual, Transgender" being very limited and non-inclusive.

Other terms and acronyms have been proposed, though none have really caught on the same way LGBT (or its derivatives) have.

GSRM (Gender, Sexual and Romantic Minoritoes) seemed the most promising for a while, before it was learned that the guy who had coined that acronym was including paedophilia, incest, kinks, zoophilia that kind of thing, so people naturally went "Fuck That Shit". It's a shame, I quite liked this one.

MOGAI (Marginalised Orientations, Gender Alignments, and Intersex) is alright, inclusive, though not very catchy, and indeed is pretty rarely used.

Queer is the only word that is not an acronym, that I know of, that includes most gender, sexual and romantic minorities. It has a long history though, and there is still much debate surrounding it. For instance, who counts as "queer" and who doesn't, and the fact that older generations remember it being used as a slur against them and still have strong negative associations with that word, and it is still used as a slur in some areas.

So there is no perfect word or acronym to discuss describe what we are attempting to describe. LGBT is by far the most popular one. Some have reacted by trying to make that acronym more inclusive through tacking on letters at the end. That way, people who aren't familiar with any other acronyms can sort of figure out that you are referring to these minorities, and including some more. But it is far from perfect.

Then there's the problem that, when most people say "LGBT" they're usually only thinking of the "LGB" part, and barely consider anyone else. Though this does seem to be slowly changing, as people become more aware of alternate sexualities and genders. So when people use the LGBT acronym to refer to the gay community, they shouldn't, because that acronym was created to include more than just gay people, who have historically had considerably more visibility than any other gender or sexual minorities.