If it extends to cisgender people, who do not face the same problems as trans* people, who do not exhibit the same range of gender expression (or else they would not be cisgender), then it becomes a useless term. The whole point is that this is a group of people bound by the very fact that they *aren't* cisgender, with things that arise because of that, such as health concerns, risk-factors from bigotry and trans-bashers, etc. And I think it's a little disingenuous for you to even say that, you're smarter than that and this should be more than obvious, the same as extending "african american" to include European whites would be absurd.
I'm not sure how often I need to say this, but I'll say it again, and try to be clearer: This is about "lumping" them together in situations where they ought to be lumped together, such as a trans* pride march, talking about health-issues that face all or nearly all trans* people, talking about the problems trans* people face from those outside who view them all as "tranny fag freaks" and threaten or actively hurt them. If there are issues discussed that one sub-group faces but others don't, then you discuss it using that sub-groups term. If you know which sub-group someone falls into, then when it comes up, you call them by the sub-group term they have told you they fall under. IF you don't know, then you don't know, and you don't call them a bloody yellow-jacket when it comes up. You call them trans*, the same as if you don't know if someone is from New York or California, you say "They're American" when it's relevant. Or should we start calling you Irish? After all, you live in [northern] Ireland. You should just calm down and don't take offense over such a misunderstanding. [I realize that you will probably say you only take offense when someone continuously calls you Irish, but that's pretty much the same thing going on here, you realize that, yes? I'm telling you that trans* is preferred in the circumstances such I've described, and you turn around and say "It doesn't matter!" or "How exclusive to not make the term hilariously useless!"]
This isn't about "honest mistakes" or anything like that, you asked what purpose the term serves, and this is that purpose. As I said, if you make an honest mistake such as misgendering someone, own up to it, have no malice, and make best effort to rectify that, there is *no* basis for any ill-will or judgement towards you. If you do not do any of those, then there *is* basis. Though I feel the need to reiterate, this was not about honest mistakes or misgendering, but about the question of what purpose the term serves, and why you shouldn't just shotgun a term at people and hope they'll speak up and say "Uh, hey, that's the wrong term, you know." Though, again, trans* is not often used in casual conversation, unless it comes about to discussing trans* issues. Usually the main issue in those contexts is the misgendering. Trans* is used as a discussion tool to discuss issues that face trans* people, or to discuss someone who you don't know what they are beyond them not being cisgender.
The communities bit was explaining why trans* people would feel loyal to those communities, and that there is nothing wrong with people identifying with a community, which you seemed to find issue with in regards to "I'd feel insulted if I was transgender and called part of the transgender community."