The size of your emergency funds will determine the level of problem or emergencies that it can solve. You can't have $500 in your emergency funds account and expect it to solve a problem of $1000. It is wise for an investor to continually add to their emergency funds account as they keep getting resources. It is simple logic, it doesn't have anything to do with believe or whatsoever.
Your emergency fund is proportional with total money you have. Assume you have only $1,000 totally, you can not assign an emergency fund with $1,000 or 10,000 but it is possible to have an emergency fund at $100,000 if your total wealth is several billions of dollar.
If you have plan to add up more money to your emergency fund, it's good and you also have to be clear that how much is acceptable for your emergency fund and when you reach that point, you can feel safe enough and reduce severe need of adding more money to that fund. It's good if you can add more money to it but after that safe point, it's not terrible if you won't add more money for it.
Living without money for emergency fund is bad for everyone especially people who are ready to spend money for luxurious things and don't mind to build up their emergency fund.