Yes, but you may notice that your approach does exactly what I said, it requires parsing the entire expression before you can determine the proper operator precedence. Up through the eighties there was a lot of discussion among compiler creators about ways to short cut this process, because resources were limited and a complete parsing wasn’t always possible. By the eighties this problem was only showing up when the calculations were complex, but it still existed. Even today, many people rightly don’t trust the compiler to properly evaluate operator precedence. Now it is less to do with resource limitations and more to do with the fact that people with modern computer science degrees frequently have very poor math skills.
BTW, this is one reason I still love and use my HP15C, it is one of the few calculators where the math functions have actuallly been tested and proved (with a couple of minor exceptions) to actually produce the correct results.
RPN is hard for people to learn if they first learned algebraic method and are poor at math skills to begin with. Several generations of engineers learned it with little difficulty. While I love FORTH, it isn’t popular for more reasons then just RPN calculations. SInce it basically allows every programmer to create their own language, it was a nightmare for program maintenance…