Temperature coefficient MOSFET vs. temperature coefficient of BJT
I do not know the answer to your question about physic behind this. 

But your statement about MOSFET temperature coefficient is only true when MOSFET work as a switch. 

In linear region (saturation) most MOSFET will have as a  negative temperature coefficient as BJT have. 

And in general terms, the MOSFET can have negative, positive and zero temperature coefficient. 
And we can see this on Transfer characteristic Id=f(Vgs) in the datasheet.

   

More here 

https://www.infineon.com/dgdl/Infineon-ApplicationNote_Linear_Mode_Operation_Safe_Operation_Diagram_MOSFETs-AN-v01_00-EN.pdf?fileId=db3a30433e30e4bf013e3646e9381200

https://www.onsemi.com/pub/Collateral/AND8199-D.PDF  

And here I found a specially designed MOSFET for audio amplifiers application.

http://www.exicon.info/PDFs/ecw20n20-z.pdf



As you can see for this lateral MOSFET if you set the quiescent current at Id > 0.2A you are in the safe zone (zero or positive temperature coefficient) 
And no temperature compensation network is needed.