The height restriction is for safety purposes only regarding blocking the door exits in an evacuation. You must be able to reach the assist handles either side of the 747 door to guard and block the door in emergencies.
Unfortunately if you are below a certain height it pretty much means your arms are not long enough to do this.
I have had many friends miss out on the opportunity to fly with certain airlines because of this. If your passion is to make your living in the sky you just need to find an airline with smaller aircraft and lower height requirements.