Because sometimes you can drop words without running the risk of being confusing, often because the context fills in the blanks.

For example, if I write something and John responds "That's interesting. Would love to talk to you further about it" -- it's not made explicit who would love to talk, but who else than John could it possibly be? If on the other hand John's reply reads more like: "I liked your post, and my friend Steve found it particularly interesting. Would love to talk you you further" -- in this case you risk being confusing, because would John or Steve like to talk to you?

There's a similar effect with a sentence like: "That's an interesting observation. Might be good to get some more data." You've shortened "It might be good...", but that's OK since there is no risk of confusion.

I've rarely heard this in verbal communication. Much more common is the contraction, "I'd love to talk to you about this further."

The only time I've really seen this is through written communication, including instant messages, texts, informal letters/postcards, and informal emails. In each of these forms, sentence fragments in general are very common. I've also seen this more and more in formal written communications over the past few years, but usually from people who regularly use the aforementioned informal written forms of communication.

I'm not really sure, but I think it's because a lot of my "dialogue" is internal, and it's annoying to put pronouns in there when it's always first-person. E.g. "I should do the dishes" or "I'd like to see what happened to that HN conversation from earlier." I just think "hm, should do the dishes" and sometimes I talk that way out loud. I know it's really confusing though, because if I say "should do the dishes" out loud, it sounds like I'm telling someone else to do the dishes.

I don't mind.

I think this make it more colloquial, hence more personal (at least to some).

Like "Wanna lunch"? You most likely would prefer that over a fully formed, grammatically correct subject line.

Or as we say in Pittsburgh, j'eet yet?

I've noticed this habit in personal emails about startup-related chitchat. It could be unique to the tech scene that we all unconsciously reuse in order to self-identify. I'd be curious to see if data can back this up as a trend.

What about 'touch base'? For me, base seems to get touched several times a week.

Something that nobody else has brought up so far is that certain media start off with the username.

Facebook, irc, etc al, all give you the subject. So it looks like 'bmelton would love to talk to you about', and such.