Reasons:

1. Because it's so natural for people to do! And Alexa is a product for people.

2. Users quite often start to speak while Alexa is still speaking or just finished speaking and haven't yet turned on its mic.
   There is a blue light, but sometimes users speak to Alexa when it's outside of their view site. Alexa is designed to be for eye-busy experience, and eyes might be busy while interaction.

3. Alexa is actually listening to users all the time while it's speaking - but now it only detects a wake word. So why don't allow a full intent there?

4. Short input is missed sometimes - as users finish speaking BEFORE Alexa starts to listen.
   Users are not happy, so devs are not happy neither.

5. When Alexa is talking it means that users want it to talk, so it's normal NOT to use wake word.

I have a skill that faces problem of people start speaking "too early" for Alexa. And I end up adding more and more "synonyms" into my model to handle this case, e.g. for Rihanna I needed to add {hanna, anna, na}. It seems like an artificial thing that needs to be taken care. And short input as "Abba" is often completely missed with no way to recover.

If you as a dev also face this problem or just think it's fair to have such feature, please upvote!