You just need a tool that's adaptable and will let you parse-as-you-search. Without a schema, your logs can change whenever, and you can still easily derive value from them.
If you don't know that your service is down, then you don't know where and what to look for. for monitoring, you need to be looking for a specific parameter or string. if that changes, its very difficult to generate an automated alert.
Ideally you'd have a schema that you agree company wide. Before an app is deployed it has to pass the schema test. At least that would cover most of the basic checks.
but, For most small places, logs are perfectly fine for monitoring, as you imply