I differentiate between savings and investments. For example, my own savings give me the ability to modestly live for 1 year without work AND without liquidating my investments.

If I had everything invested and nothing saved in bank account, I might get into situation when I need to liquidate my investments ASAP, which could be very unfortunate, timing-wise.

I agree that your house is in itself not savings and that taking out a mortgage to buy property doesn't count as savings, and one can have long discussion about if and when taking out a mortgage to by house is a sound financial decision. However once you have the house and the mortgage, then paying down that mortgage is savings, just not a very liquid form of savings. You can argue that it isn't the best and most efficient form of saving and depending on what the interest rates are and where you think interest rates are going you might be able to do something better with your money, but that is beside the point.