Even in my very secure environment (at work and home), I have the ability to use Windows Task Manager to set the ArcMap session priority higher; it always defaults to Normal. Access this from the Task Manager Details screen. This will last until you completely exit the software, so you can switch MXDs but still keep the higher priority.
But what you are describing is a little strange. I often load empty ArcMap, then choose a project because everything starts up better that way. I don't think the "empty" map that comes up is entirely empty though, since the software is looking for your Normal template. At 10.6, mine is in my profile at AppData\Roaming\ESRI\.... So maybe try finding, then erasing or altering your Normal template.Also not signing into ArcGIS Online may help.
