Wealth creation requires many stages of money management, which are the making money, managing money and growing money. If these categories are mastered then it's possible to attaining a wealthy investment plan. Saving money is the vital point of beginning the journey of wealth creation because it makes an investor feel calm with energy to strategy itself the way out.
You just made a healthy explanation of what wealth means, growing money is the strongest part of becoming wealthy. Paychecks don't last even with savings can soon go bankrupt, might be a big earner whereas having no alternate source to generate money restrains from achieving the wealthy status. All wealthy people are investors, non are working class or still works under where they get paid monthly doing a 9-5 job.
If you are a great earner, as a worker, then the logical thing would be that you would be able to save enough to have a recurring income eventually from your investments, if you haven't done that then you made a mistake.
Imagine a person who makes a lot of money, if they are not stupid and spend all of it, then all they have to do is save some aside and after they save some aside, they can invest it on something that can make them some money. Here many people are not American neither, but let's assume we are American, if you are making 100k a year, which isn't wealth or rich, you could still live off 80k a year (after taxes) if you live in not New York or California, in many states 80k is ok. Then you take that 20k, save it for 2-3 years, then use 50k as basis if your investment, get a loan, buy a house, rent it out, and then repeat this plenty of time.