What is meant by elasticity is that you can handle varying load on demand. You don't need to provision/scale for spiky/unexpected loads in advance, your infrastructure will expand and contract on demand. This is a very difficult problem to solve.

Also, this is on a much different scale than a small queue on a mobile app like you are comparing it to. A queue on a mobile app doesn't really need elasticity or scale. But when you're dealing with millions/billions of messages, the complexity is on a whole different level. And providing the ability to scale/grow with zero effort is extremely compelling.

Now if you had millions of users of your mobile app and they all sent messages for processing, an elastic, scalable message queue would be a godsend.