Agreed that X seems to have caught on by being more visually striking than E, while being pronounced the same as and almost certainly standing for ex-. An E in the same places would likely take a bit more thinking to work out.

Similar examples are the Q in the abbreviation BBQ for barbecue and L for Chicago's el-evated trains.

(This is different from x for trans- in transfer and transmit, where x seems to be used as a drawing suggestive of two things crossing---like the x for cross- in xing for crossing; and the X in Xmas, where X is Greek chi, first letter of Christ's name.)

Because an "ecks" is an "ecks" whether preceded by an E or not.

Therefore, it is about the only logical choice when it comes to "abbreviating" the syllable "ex-".

Consider that abbreviating is not necessarily the same thing as initializing, which is only one method of abbreviation among many.