I am trying to create a column in a table that\'s a foreign key, but in MySQL that\'s more difficult than it should be. It would require me to go back and make certain changes
They are quite important. You don't want to define your model entirely through PHP. What if there is a bug in your PHP code? You could easily have null'ed columns where your business rules state you should not. By defining it at the database level, you at least get that check for free. You're going to really hate it when there are bugs in your PHP or if any other tool ever uses your database. You're just asking for problem, IMHO.
Be advised, this is the very short version of the story.