One other reason this is not a viable option is that children aren't always with their parents. My son is old enough he is out with his friends, with his coach, or other lay people. I could handle drawing up epi, but I guarentee his football coach wouldn't want that responsibility, and no offense to him, but I wouldn't want him to do it either.
Next time I need epi pens for my son I will look into the adrenaclick, the old style of epi pen had a needle that stayed out and as someone else mentioned after administration I bent back the needle and put it back into the hard plastic sleeve it came in.
Having easy to administer epinephrine is of utmost importance, because if it isn't given quickly that person that needs it could be dead.