It would be cool if there was an option in Bitcoin Core for disabling the system tray entirely.

{
    showNormalIfMinimized(true);
}
void BitcoinGUI::detectShutdown()
{
    if (ShutdownRequested())
    {
        if(rpcConsole)
            rpcConsole->hide();
        qApp->quit();
    }
}
void BitcoinGUI::showProgress(const QString &title, int nProgress)