Alternatively: could selling out be a method of potential advertisement?
"If they sold out, the product must be great!"
"If they sold out, the product must be great!"
2) I bet that the average cart size at checkout is less than half of the cost of an Echo.
The benefits don't outweigh the costs of a marketing stunt of claiming that they are sold out.
Birthday is different though, but will not be the case for most decisions.
Long term gains > Short term gains on a product like this.