Why is the subject omitted in sentences like "Thought you'd never ask"?

This is due to a phenomenon that occurs in intimate conversational spoken English called "Conversational Deletion". It was discussed and exemplified quite thoroughly in a 1974 PhD dissertation in linguistics at the University of Michigan that I had the honor of directing.

Thrasher, Randolph H. Jr. 1974. Shouldn't Ignore These Strings: A Study of Conversational Deletion, Ph.D. Dissertation, Linguistics, University of Michigan, Ann Arbor

To quote:

• (1.16) Gotta go now.
• (1.17) See you next Tuesday.
• (1.18) Too bad about old Charlie.
• (1.19) No need to get upset about it.
• (1.20) Been in Ann Arbor long?
• (1.21) Ever get a chance to use your Dogrib?
• (1.22) Ever get to Japan, look me up.
• (1.23) Good thing we didn't run into anybody we know.
• (1.24) Last person I expected to meet was John.
• (1.25) Wife wants to go to the mountains this year.
  [all from Thrasher 1974 p.5]

"The phenomenon can be viewed as erosion of the beginning of sentences, deleting (some, but not all) articles, dummies, auxiliaries, possessives, conditional if, and [most relevantly for this discussion -jl] subject pronouns. But it only erodes up to a point, and only in some cases.

"Whatever is exposed (in sentence initial position) can be swept away. If erosion of the first element exposes another vulnerable element, this too may be eroded. The process continues until a hard (non-vulnerable) element is encountered." [ibidem p.9]

In general, exposed first-person subjects are vulnerable in statements, and second-person in questions; and any exposed pronoun is vulnerable if it is recoverable from later in the sentence.

• (3.2) Can't do it, can {I/you/he/she/they/we}? [ibidem p.59]

Let me reiterate that this phenomenon only occurs in speaking English, and in other informal communication systems like email and txting that work like speech. It is not good formal written style, except for reporting dialog in a story.

The "implied" subject is a common feature of conversation and some writing, especially fiction (not necessarily limited to dialogue). Where the subject is clear, it is frequently omitted. This is a form of ellipsis.

Great. [For "That's great."]
Such a waste. [For "That is such a waste."]
Coming! [For "I'm coming."]

There are many more. In each case, the subject will be understood, usually from something someone else has said.

Person A: You don't have time to talk with Martha.
Person B: Not true. I've moved my schedule around.

There's even a famous advertising campaign in the U.S. featuring people from different walks of life who are sporting a "milk mustache" (milk on the upper lip from having recently drunk some milk). The headline? "Got milk?"

But the implied subject is most often seen in imperative statements:

Go now.
Stop!
Get up.

In the above, the subject is you, and is hardly ever included.

The Principles and Parameters theory of languages might answer your question.

According to this theory, languages have certain parameters that can be either on or off position. The property you are asking about is known as the pro-drop (pronoun dropping) parameter. Spanish is pro-drop, but English isn't.

There is another parameter called verb attraction. The interesting thing is that all pro-drop languages are also verb attraction languages. If I understand the theory correctly, there are good reasons why a language with the pro-drop feature must have the verb attraction feature.

So if you believe the Principles and Parameters theory, English cannot gain the pro-drop parameter until it has gained the verb attraction parameter.

All the counter-examples given above are, presumably, exceptions that prove the rule.