Possible workarounds include logfile streaming (say via a pipe on the filesystem) but that introduces much larger problems and would in no way be compatible with the app rolling its log files.
What you call a workaround (streaming to a central location via syslog or scribe) happens to be the standard approach in my corner of the world. Analytics and monitoring operate naturally on the stream because, as you point out, sampling on rolling logfiles is not exactly reasonable, neither is scattering logfiles across application servers.
I'm leaving this discussion at this point because I'm not interested in your condescending tone and insults. It appears you haven't even centralized your logging, yet feel entitled to give ops-advice that is at odds with how the rest of the world operates.