For the past decade, saving money would get you nowhere. It might change now as long as interest rates stay where they are at but if you started savings by putting little by little of your extra funds In a savings account, most of that money would of evaporated due to inflation.
This is why most wealthy people aren’t affected by inflation because they own assets like stocks, real estate, gold, bitcoin, etc.
This goes to say that saving will not get us wealthy but investing is. Although we don't really aim to be financially wealthy but at least we can secure and enjoy our future retirement and we can leave some inheritance into our offspring. That's exactly the reason why we don't just need to focus on enjoying the present life, but we should also learn to navigate our future as well by saving and investing from time to time when opportunities are available.
When you are talking about wealth I don't think you can take away savings from the picture because savings also plays it own role. Without savings I don't think it is possible to carry out investment expecially for those who earn small, savings have to be done for investment to take place. The only way I see savings as something that won't have any value is when saves money for a long period of time and not making any plans on investing.
Saving is very important for people who receives low income for them to be able to start up any investment. The main purpose of savings is to make investment but it will be unwise when saving is done continously and no investment because the money will lose value due to inflation.