Investment shenanigans excluded, if you have enough savings to pay off your mortgage in case you lose your job, there's no point in getting a mortgage in the first place.
You're poisoning the well there, as that is the major reason to get a mortgage even when you have enough cash to buy a house outright. It's not "shenanigans", it almost always makes financial sense to keep your cash invested elsewhere when mortgage rates are low.
Sometimes I wonder how people manage to browse the Web without encountering "common" pieces of wisdom. Maybe we should bundle up a bunch of useful YouTube/TikToks as a supplemental education package for students.
So the gamble is, do you spend 2 years saving up for 6 months of income as a buffer and send tens of thousands of dollars down the drain in the meantime, or do you roll the dice and hope nothing bad happens in the next 5 or so years? The people who end up in the best position will be those who take the second option, and most of the time it will work out.
Also don't forget taxes, insurance, mortgage interest needs to get paid while house is in your hands. Most mortgages have lots of interest during the first few years.