What is the point of writing
The character count is the same, so where is the profit?
It makes it easier for a reader to imagine the tone of the speaker.
Consider these two utterances:
For some reason, when I read those two sentences, it's easy to imagine the second person as less articulate, less well-dressed, less well-groomed, less well-educated, or less calm and collected. Not all of those inferences may be true – more context would reveal which of those assumptions are accurate, and which are erroneous, but, for the most part, those are the impressions I begin to consider.
For example, if this was the beginning of a conversation between a successful businessman and a taxicab driver, I might expect the story to begin with the first sentence if the businessman was telling his story, but the second sentence if the cab driver was starting his narrative – although that would not always be the case. (If an author wanted to portray the businessman as panicked and distraught, it might go the other way around, for example.)
Other literary ways to accomplish the same thing might be subject-verb disagreement, using alternative spellings, or shortening minor words such as of or and:
Such modifications aren't always tied to, say, a speaker's education level, but they are sometimes used be to emphasize a local accent as well.
Listen to Leonardo DiCaprio's character just a little past 62 seconds into this movie trailer. Grammatically, the sentence is:
However, if I wanted to write a script that shows the line spoken the way Leonardo says it, I might write:
My spell checker gives me three red lines in that one sentence; however, it's much closer to the original line as spoken by Mr. DiCaprio than the so-called correctly spelled version is.
This is often referred to as g-dropping. It doesn't actually involve dropping a /g/ sound, though; it's intended to represent the replacement of the usual <ng> sound /ŋ/ (a velar nasal) with the <n> sound /n/ (an alveolar nasal).
In other words, bloomin' represents the pronunciation /ˈblumɪn/ rather than /ˈblumɪŋ/. It's about sound, not about making the graphic representation of the word shorter. (You're right that if that was the goal, it wouldn't be very successful!)
This "g-dropped" sound is considered more informal or colloquial, and it's almost never represented in writing in standard English. Avoid using it yourself if your goal is to write standard or formal English. You'll most likely hear it quite often in conversation, however; it's part of almost every dialect of English.
One final note: even when it's pronounced /n/ rather than /ŋ/, it will most commonly be written <ng>. It's never necessary for you to write <n'> yourself, although if you're in a sufficiently informal situation such as chat online, you could choose to do so. Just be careful not to use it when it's inappropriate!