Especially in non-development communities, people often uploaded cool thumbnails of themselves in a “welcome to my profile” setup. I’ve noticed that user pages have diminished in customization; my profile page doesn’t feel like my own anymore.
Plus, the form-factor of a full scaled thumbnail is already there; why not blow it up instead of using a tiny square thumbnail?
For the second part, it is done to be mobile “compatible”. It isn’t always that much rectangular, so whole thumbnail can not always fit in well.
Well, lots of websites scale up and down based on screen size.
But they’re only icons, and icons are square.
It’s the most fitting way. I don’t see a problem in fitting the thumbnail into the icon format 
Never understood why the large rectangular space perfect for the games image had the square icon on it. It’s like having a widescreen TV with a tiny show thats the wrong resolution in the middle.