thousands of hosts costs hundreds of thousands of dollars. a few thousands more is a low barrier.
Sumologic, papertrail, logentries (and many more) for cloud logs. Graylog or ELK or Splunk for self hosted logs.
However, logs should never be send to the cloud, they are too sensitive information to outsource. Server metrics + stats are more reasonable.
Agree, stats and logs cover different things. Need both.