‘Twas good until ‘twasn’t

My take is that it is not so much a matter of the language proper as of what goes with it in terms of connotation that is often quickly picked up or associated with a person as they speak, such as regional background or (not saying that this is politically correct, but it is observable as a matter of fact) what is called social class. Variations in speaking like “‘twas” and “‘twasn’t” would easily fall into that category in some places.

Variations of speech that are not standard language have for long stretches served, or been seen by some parts of society at least, as a social marker telling of, say, a less educated person. A speaker not wishing to be associated with such connotations (and conscious and capable of avoiding them) may choose to avoid some variations of non-standard language.

A speaker's choice of using certain features or variations of language may also be a question of register. Note how many people choose their words differently as they speak with family or close friends, "in the hood" (:D), within a special interest group, or with complete strangers on different levels; there would very often also be differentiating between, say, particularly respected persons, persons in a position of power or highly superior to the speaker e.g. at the workplace, colleagues and (hopefully not often) "all the way down" to the janitor and the person who was hired to clean up the office and take out the garbage.

Some choice of register may also be deemed inappropriate in certain situations, such as where formal language would generally be required (or expected), one example of this would be, for many times at least, in court.

Some would also consider many kinds of abbreviated speech to be just sloppy and overly casual.

To complicate the matter, things have not been the same in all ages. Speech that was perfectly normal in, say, the Shakespearian era could sound pretty outdated today. A contemporary speaker might employ contemporarily uncommon speech selectively to give their message a specific note, but in general, it would often just sound weird.

All of this would go to significantly reduce the number of opportunities to use abbreviated speech. That would obviously explain why it would generally not be completely absent, but still seen considerably less than what would be theoretically possible.