I'm not sure if I can give any better answer more than what you are supposing is true, but I just wanted to express my agreement with you (that it was just for convenience among those who share a common understanding of the language), and maybe offer some meaningful insight into the process of contractions being created and becoming more and more common over time.
For example to understand common spoken American English, it seems to be essential that you be very comfortable with expressions like I'M GOING TO... becoming I'M GOING TA or most commonly, I'M GONNA. I'VE GOT TO... becoming I'VE GOT TA or most often I'VE GOTTA, and, of course, I WANT TO becoming I WANT TA or usually I WANNA. Then these are usually followed by verb phrases that can be equally confusing the more that they are contracted... often beyond what we usually can even fully express in writing. Some examples of a contraction that is so common most American native speakers aren't even aware that they're making a contraction at all--skipping the "H". : "ASK 'IM (him) to COME OVER". "TELL 'ER (her) to CALL 'IM (him) BACK" & "GIVE 'IM (him) 'IS (his) book back". But each country where English is spoken as the native language has its own version of these things, it seems...so the best we can do is do our best to "go with the flow" of 'em (them) and "get the hang of 'em" (them) the best that we can.
The examples of contractions are nearly endless, but it seems to be something that just happens...the more the same phrase or expression is used, and the more condensed versions seem to make their appearance for convenience...but also for creating a special sense of mutual understanding among certain people of a certain area or ethnic background. It just seems to be human nature.
My background of growing up in Japan taught me that each group of people on each side of a mountain (of a very mountainous country) usually developed a very distinct dialect with many mutually-understood contractions that people on the other side of the mountain couldn't understand... and so there are maybe dozens of general area dialects, and maybe hundreds of distinct ones that have developed over hundreds of years of generations of people "living on their side of the mountain" there.
The same seems to be the case in the UK where not only the Scottish and Irish each have their "take" on the English language, it may even come down to which part of each of these places you are from or even which side of London you're from. The same seems to be the case in New York city in the US where local people can tell which side of the city you're from by the way you use certain contractions and inflections. Maybe no big answers here for you, but still hopefully some interesting things to think about as we deal with the many odd things about learning a language and wonder why there has to be so many different ways to say things...and shorten things!