I strongly disagree with your point of vue. I think saving money is not something really important.
Maybe it's because i'm French so i don't have to care about "medical emergencies" as you say, cause of course if you're not reinboursed by your gvt you're right it's important to save some money in case you or one that you love needs it :/
But saving money for investment is not really a good deal, if you have a good investment opportunity, just take a loan. It's faster, easier and you can invest a real amount of money (not just a few thousands dollars). I invested in house location, i borrowed 150 000 euros and built a house then rent it. It covers 95% of the loan payment and i pay the rest.
But i suppose it depends a lots on your personal situation and xhere/how you live
