You also mentioned having a separate minute dial. That also exists. There are watches with multiple dials, some for the seconds, others have dials solely for stopwatch functionality (chronograph watches).
Ultimately, I sort of see what you are saying, but I think if you do some research, you'll see solutions do exist.
Also, part of what makes people love watches (including myself) is the engineering behind them and the beauty of their design. For accuracy and functionality, I'll take my G-Shock over any analog (and automatic/mechanical) watch. However, I don't wear a watch purely for accuracy and functionality. They provide a bit of both, but there is more to it.