Yes there are several reasons.
This blog post explains it about the Echo and the wake word Alexa. I'll summarize a bit.
Wake word recognition is done locally and in real-time. That limits the lengths of the wake word due to obvious processing limitations. Furthermore users don't want to recite a poem to activate the smart assistant. Thus, it has to be short.
It has to work with an almost 100% accuracy when called and also not recognized with that certainty when not called for. That makes problems and also makes for a minimum length for wake words. Amazon's choice to allow Echo is quite surprising since it's just two syllables.
If we look at the usual suspects, we have Alexa (3 syllables), Amazon (3), Echo (2), Ok Google (4), Hey Cortana (4), and Hey Siri (3). All industry giants almost agree on three being a good choice number of syllables.
Strangely enough the most wanted wake word "computer" has also three syllables and would match that requirement easily. It's also not trademarked.
As the blog—and reason—tells us, we totally want to avoid false positives. Let's have a look about how established the words Computer, Siri, Cortana and Alexa are. This is the Google book corpus from 2008.
Exactly, Siri and Alexa are virtually flatlining against computer and Cortana gives an error. Not found. Makes sense since the corpus is from 2008. To give us some more perspective why computer is a terrible wake word another graph.
This Ngram shows the two most popular US baby names of 2016 (for currency), as well as Tom and Dave also flatline against computer. Queen, basketball and police manage to register properly. Anyhow this gives us an idea why Computer, Earl Grey, Hot hasn't been allowed so far. People use the word computer way too often.
One more thing about false positives. Alexa rhymes with virtually nothing one would say.
Computer rhymes with 74 things.