Not true. QMS does keep its house clean by regularly running a job that removes all logs files older than a specific number of days. The default is set at 30 days. If you don't like that, you can change the default by editing a key in an XML configuration file. The config file is called QVDistributionService.exe.config and it is located in the installation directory C:\Program Files\QlikView\Distribution Service, so NOT in the C:\ProgramData folder where you would expect it.
Open the file with a text editor and locate a key called NbrOfDaysToKeepQDSLogs. That's the one.