Why should you follow a poor lifestyle if you are wealthy? It doesn't make sense to me. I'll also tell you one thing. If you live a poor lifestyle but benefit society a lot, you'll simply suffer and in the end, no one will appreciate your efforts. Just look at multi billionaire businessmen who don't appreciate their own workforce, they are still praised by the society (Jeff Bezos for example and his attitude towards amazon workers).
No, my opinion is to enjoy the life at its fullest. You can do good things but your own self should be the priority because in the end, your good efforts will barely be appreciated.
You know one thing with the society, if you have billions in your name and they don't see that millions on you, they are not going to value you, they will not respect you and they may see you as someone that is poor when in fact you can take care of them. The world functions when they see you have something and the better way you can demonstrate it is when you show them that you have it and that's the only way you can penetrate through plenty of opportunities.
I don't care what the world thinks, if I have money I will live the life as it fit my financial status, if I have the money I will get the best life for myself and I have nothing, I will not pretend that I have an asset. The way OP describe wealthy people should leave like they have nothing, the same way some people fake life, they don't have what they claimed they have, that's what the common social media is about today, fake lifestyle.