I totally agree. We never taught the alphabet until much later, when she was already able to read many words.
Once she has already seen those 'symbols' so often (from learning words), it's much easier to learn what these things are called and the sound of them since they are something that's already familiar, not to mention if they have already been intuiting the phonic rules, a lot of what you then teach them about alphabets would also make a lot of sense and be much easier to teach.
(gosh, hope i made sense there!

)