I never remembered having an emergency needing $500,000 or even $5,000. As far as I can remember recently, my biggest emergency spending is around $1,500 and that's when my 13-year old water heater leaked and needed replacement. DW Dad passed away - plane ticket & expenses was $1,200. Getting sick suddenly - medical insurance took care of most. Copay for emergency room was $100 and after diagnosis walked out the same day. Blew a tire - $200. I pray I don't need a big emergency, but there's the entire nest egg if needed. Can always sell stocks, bonds, etc ... in a few seconds.
You can have a $1 million or $10 million in reserve, a reserve Jet if you need to fly to get away from catastrophe, a reserve house if your house got hit by a meteor and still not feel safe. Feeling safe is all in the mind. You could croak tomorrow in your sleep and that's the end of it. Just go thru life without so much fear and I think you'll be ok.