We all know that the English alphabet we use today didn't come to us fully-formed. It evolved over thousands of years and was changed and adapted as needed. Letters have been added when needed and dropped due to lack of use. The design of each letter has changed over time. Even the sounds of those letters have changed. In fact, each letter has its own story. So the way we ended up with the alphabet as it is is kind of messy. If it were designed today from scratch, it wouldn't be at all like the ABCs we know. A modern-day critique from Randall Munroe at xkcd shows us why.
Good points: vowel spacing, and that song is fun to sing. Bad points: quite a few letters that aren't necessary, and the order is funny. Still, how could we improve it and keep that song that we all know? At least it rhymes! Maybe the alphabet is just fine as it is, and Munroe is our patron saint of overthinking everything.