Because logs are primarily unstructured data, they are well suited to batch data analysis of a discrete event. However, a big data approach to logs makes them poorly suited to the real-time search and stream processing required for timely alerts. The high volumes of disk I/O and network load needed for log exploration are much better aligned to post-hoc analysis, as opposed to the high metric throughput typical of a time series database used for infrastructure monitoring.
For cloud environments, whose goal is to scale infrastructure elastically, you need a purpose-built system focused on metrics and analytics. Real-time aggregation is a job not fit for batch analytics because alerting requires much faster, more flexible insights. Log analysis for deeper exploration and investigation is ultimately a great complement to an infrastructure monitoring solution that handles real-time analytics and alerting on time series data.
With the real-time insight introduced by modern infrastructure monitoring, application developers, infrastructure engineers, and operations teams can collaborate across the entire application lifecycle for the first time, from pre-production performance engineering through real-time service-level monitoring in production to post-mortem investigation of past issues.