"Nobody uses real stopwatches anymore" might be somewhat true, but in athletics training they still do, and it just shows that it's not possible to adequately reproduce a thing on a touch screen and have it be as functional as the real item. A stopwatch app on a phone will always be a poor substitute for a real stopwatch.
On a touch screen you have to hover your finger over the button and move it down some indeterminate distance to actuate the button. The equivalent to the above example for a touch screen is to activate on release, as you can rest in a state “ready to click” just like on a physical button that way.