The 10-second rule is actually a guide to ensure that you are serving the freshest shots of espresso to the customers, and to provide some uniformity to the business.
Imagine if there is no guideline set, and baristas just do whatever they want? Can you imagine the possibilities?
Regardless of the machine used, the 10-second rule is just there to guide baristas. Flavorwise, there is indeed a difference if you use a shot standing for more than 10 seconds rather than a freshly drawn shot. This change in flavor is essential if you want to keep your drinks standard, i.e., the same taste regardless of who prepares it.
Now, if you have customers who prefer a different taste, that's when you may do some tweaking in order to customize the drink.