Why is it absurd? Bit optimistic, perhaps, but not absurd.
I wouldn’t say “wrong”: just don’t use it in formal situations.
Well, I grew up in southern Ohio and my mother is from western Pennsylvania, but my father is from neither of those places, so I have heard (and used) both “the car needs washed” and “the car needs to be washed” (or “the car needs washing”) all my life. Both sound fine to me. Since I maintain that “needs washed” is not wrong, I continue to say it even here in the Pacific Northwest, but I admit that now I do it to see people’s eyes get wide (“he didn’t really say that, did he? But he seems so educated!”).
I imagine I can; the reduction applies only to “passive infinitives”, which “to be gone” is not an example of. “The dog wants let out”, I imagine, would be more acceptable to your ears.
(Note, everyone who needs to, that this is a clear example of how even non-standard varieties of language have systematic grammatical rules, same as any others. It’s not anything like “Drop words as you slothfully please”.)
I want drop words as I slothfully please.
“A Bradypus, or sloth, am I…” 
Well, alright; as long as you continue to show such restraint, I guess I’ll file the paperwork to allow it. But don’t make me regret this!
I promise faithfully retain word in my sentences except those which come verbs.
I think it’s oversimplification to say the usage is “rural”. It gets pretty rural ‘round these parts, and you’d be most likely to hear "this dog needs washin’" or “this dog needs a washin’” or even “this dog needs to be washed”, but not really “this dog needs washed”. I don’t think anyone would look at you askance for the latter; it just wouldn’t be what we usually say in Middle TN.
Yes, there is a deletion there. You are just comfortable with it. The sentence is a fragment if those words are not understood to be there. Calling it imperative does not mean they are not there, just that the imperative includes those deleted words.
No, that’s wrong. The imperative is an entirely separate mood from the indicative, not simply a contracted version.
Adding “I order you to…” to “Pick up your socks!” changes the meaning of the sentence.
Missed one.
Where?
Fascinating thread. I married into a Western PA family. (I grew up in Eastern PA, but my mom is an Italian from a Jewish neighborhood in NJ and my dad from rural Washington state, so their accents had zero generational effect on me.)
Slippy, Dippy, and Gum Bands are all in our regular usage now–the first two ironically, the last one restricted, for some reason, only to pony-tail elastics (all others are “rubber bands”). My wife usually corrects herself when she uses “needs fixed”, but not always. (“Your grammar needs fixed,” I usually joke.) She, thankfully, never caught her dad’s pronunciation of “worshed.” Or her mom’s usage of “yet”, meaning “still” (“Do you want more of this chicken yet?”), which always confuses me for a few seconds.
The most fascinating thing in that Wiki article was the “Pennsylvania Dutch question”–a falling pitch at the end of a question to which the speaker already knows the answer. I’ve heard my FIL do this, but it never registered as a “phenomenon” until now.
My parents are from the Reading area, and now that I read that I do recognize that pattern from them.
I suspect KneadToKnow misconstrued you as deleting words before verbs, rather than, as you are actually doing, deleting those after verbs.
Of the speaker who says “This car needs washed”, we could conceivably analyze this as an entirely separate construction from “This car needs to be washed”, not simply a reduced version (whether this analysis would have some semantic reflection would be besides the point; it could plausibly be fruitful in other ways). After all, it’s not that he meant to say the latter and just left out part; it only looks like a reduction in comparison to something else. To him, there’s nothing missing.
In my experience (living in central PA for 8 years), the pitch at the end of the question may fall regardless of whether the speaker already knows the answer.