See my other comment. Logs are just one small symptom of a larger problem of poorly integrated very complex services where the complexity is pushed onto the users and not properly managed by Amazon. Which sounds very much like the problems with Azure.

My general approach is to only use the most basic services from each cloud. VMs, networks, L3 load balancers, blob storage, etc

Build the rest yourself. In many cases their higher level service is just the same open source package you would run, just managed worse.