It serves no other purpose but to have a standard everyone recognizes so if someone says they can type 70 wpm, it is the same thing for anyone saying they type that fast. If everyone used 1 letter and space for a "word", that would work too. Just has to be universal. I have one typing test which counts actual words and that test gives long words - 5 letters is typically the shortest so, with a space, it is 6. Most are longer, often by several letters. So I can't compare speeds.
I doubt the number has to do with texting word size. I think these numbers were decided on before computers were used in schools. I think whoever established the 5 characters as a word probably used data like yours back then, but since it is more complicated to calculate wpm using fractional numbers, I think that is why they chose 5. Also, 5 is much easier to calculate in your head if you have the total characters typed than using 4 or 6 or anything other than 10 - which would be way too high!