This is only like AWS Lamda if a response time of a few seconds is acceptable to you. That's the time it takes to start up an instance according to the article.
FYI - AWS Lambda cold start times are also in the seconds [1]. I'm assuming Azure functions has the same limitation. After all, code has to be retrieved from storage over the network, environment set-up, and eventually, code needs to be run. This is a limitation of physics rather than software.
Azure Functions has support now for pre-compiled functions. Start-up is fast, under 2 seconds for me and simple Http triggers.
Would be interesting to see a mashup of Azure Functions and ACI. In other words, use a event-driven trigger to spin up a container instance so you wouldn't be limited by the "serverless programming model".
[1] - https://serverless.com/blog/keep-your-lambdas-warm/