You should speak to your audience.
I'm not a paid speaker nor do I consider FC participants to be 'my audience'. They're members of FC who may or may not choose to read or reply to forum posts. I don't treat the forums as a 'soapbox', as you seem to do.
In my writing courses I was often advised to "eschew verbosity"...
There's a certain 'irony' to that specific advice, (I presume you know of it since you wrote it - never mind redefining "irony").
... but I still find myself often exhibiting that tendency.
Yep, that goes for the both of us. That's usually called, "being windy", aye?
I think we 'post' like we tend to speak (and in forums such as these when working with reply style posting it is more common to write in the manner you typically speak as you don't get the voice feedback and visual cues that you would in person that causes you to adjust your speech to who you were speaking to.
I can essentially concur with that observation.
If your audience doesn't comprehend what you are saying it is more likely that you are using poor communication skills (even if your words might be precise and fitting in other venues).
That contention, I don't concur with completely. That is, communication is a three-part process consisting of the transmission of the communication, the medium in which that transmission is communicated and the receiver of the communicated transmission. The responsibility of the 'transmitter', (the one sending the first part of the communication), is to send it in an intelligible form. That form may consist of colloquial English, (or other language), or varying degrees of precise/complex language. The "medium" of transmission in this regard is the language itself. The sender assumes the receiver can understand that language otherwise, no communication is possible. If the receiver generally understands the language but, not the specific usage or wording involved, the sender can either "dumb it down" colloquially or, not do so. At this point, it's the responsibility of the one receiving the communication to make sense of it, (how could this be otherwise? The sender is hardly responsible for the receiver's comprehension abilities - even if they personally taught the receiver how to comprehend the language, it's still up to the receiver to learn and incorporate such knowledge within their own mind).
If you wish to communicate your ideas, it is up to you to do this, not the audience to interpret them.
Obviously, I've disagreed with your declaration and stated why, above.
Being overly complex or using words unfamiliar to the audience can only cause your message to be lost. Speaking in a manner that your target understands should never be considered as "dumbing-down" and such would actually count as "wising-up".
As I previously stated, I don't consider those who read posts to be a 'target audience' when I'm replying to their posts. Nor do I agree with your contention which inverts "dumbing-down" and "wising-up" because it's illogical. Changing a message from what someone else might consider to be 'too complex/using words which are too large' certainly is "dumbing-down" a message, (and condescending to boot). My perspective being that you're not "wising-up" someone else if they aren't expending the effort to 'wise-up' themselves; you're spoon-feeding them.
Some people might think the excessive use of 'big words' (as they are often called) is a sign of arrogance ...
That assumption would be unwarranted unless there were evidence to support such a conclusion, (which excludes mere subjective perceptions and any resulting 'opinions' stemming from such internal bias). Conversely, it is more generally common for people who complain about others using "big words" to be somewhat insecure about being unable to completely comprehend what is actually being said, (even if they have some vague idea, this 'feeling' can lead to another one; inadaquacy).
Go ahead and be a proponent of 'spoon-feeding'; I'll stick with the, (possibly unrealistic), process of encouraging others to get their own 'spoons'. Remember The Matrix; there is no spoon, there is only you. <--paraphrasing