It's certainly not normal and really a bad practice in general.
Even so, there's no reason that a standard user couldn't write to some location inside of the Applications folder even if they don't have write access to /Applications itself. The installer could have easily made a folder inside the application bundle that everyone has full read/write control of.
I wouldn't use any software that does this. There's a Logs folder inside each users' Library folder for this exact purpose. If they don't follow this rule, what others are they ignoring as well?