When you are rich and people know it, they will want to separate you from your wealth. The wise man with money lives modestly and saves. Plus like you said, if everyone knows you are wealthy they will be asking for handouts. Most wealthy people also hide their wealth in companies so that they don't look rich. Elon Musk pays himself $50K a year, and lives in a home owned by Space X just as an example.
I agree in some professions you have to look the part. If you dress nicely and have a nice car it can help you out. Especially in California, there are so many people driving expensive cars here it's ridiculous. The sad part is most of them can't afford them and are putting much of their salary towards a stupid car. As I've gotten a little older materialism looks more and more stupid. Money creates as many problems as does poverty, the only difference is that being rich you don't have to worry about how to feed your kids.
Sorry for the long narrative, money is an evil that humans will never let go. Greed is engrained in human nature, probably in our DNA...
RE: Why are rich folks scared to admit they're rich?