But the infrastructure components are certainly there on AWS.
CloudWatch Logs will ingest tons of data at minimal cost. It has simple API for searching for events, but it's extremely slow to return results if you have lots of data in a LogGroup. It has a simple API to get the latest events but it has a 10s delay and its a bit tricky to get all the events from all the LogStreams in the right order.
Kinesis will ingest tons of data at minimal cost, and let you stream it back in real time.
Lambda can subscribe to all the CloudWatch Log or Kinesis Events for parsing, filtering, and forwarding.
AWS ElasticSearch can ingest all the logs and give you a richer query language and visualization tools.
I've been building all this into Convox, an open source AWS toolkit. Take a look at this CloudFormation template for an example of how to configure a CloudWatch Log Group and Lambda filter in your own AWS account:
https://github.com/convox/rack/blob/master/api/dist/kernel.j...
Also, we just use AWS for EC2 mainly.