For companies the benefits are the abiltiy to get new servers at a click of a button and get rid of a server. For example, asking the ops team to setup a snapshot of a database for a few hours while I do something is super useful.
There is also the ability to use autoscale and other stuff to automagically scale your system to handle traffic peaks. With dedcicated servers you need to always have those resources available. It's attractive to managers that they're only paying for resources when they're using it.
There are also managed services like DynamoDb, Lambda, S3, etc that can make things easier and reduce your sysadmin work. And allow you to get up and running very quickly.
Obivously, a major downside is that the pricing is extremely vulnerable to spikes like this. I think we see an article like this every 3 months or so. This one is rather tame compared to some others that were 10x as much for a 24-hour period.