> 27 bits for just one word seems wasteful

Where did you get that you need 27 bits for one word?

> Then to send any word you only need to send one number, and in binary it would have between 1 and at most 19 bits

Yep! By sorting by frequency, you are able to make it so the majority of words have shorter bit strings. By my calculations, common words such as "the", "of", and "and" will have ~4-6 bits associated with them. That means you can encode a large number of words (googling says those words make up ~1/7 of words based on frequency) with only 4-6 bits each. That's far from the 27 bits you calculated